CÁLCULO/4. DERIVADAS/1 Algebra de derivadas 1 Dada 2 condiciones determinar función que la cumple Encuentre una función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«/math» de modo que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»`«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/math».

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«/math»

]]> Hay muchas respuestas posibles, por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«msub»«mn»1«/mn»«mn»1«/mn»«/msub»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«msub»«mn»2«/mn»«mn»2«/mn»«/msub»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«msub»«mn»3«/mn»«mn»3«/mn»«/msub»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mn»3«/mn»«/math»

]]> 1.0000000 1.0000000 0 0 #sol Muy bien, ¡excelente respuesta!

]]> #sol2 La función que ingresaste sólo satisface la primera condición, es decir, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/math» pero no se cumple que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»`«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/math».

]]> #sol3 La función que ingresaste sólo satisface la segunda condición, es decir, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»`«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/math» pero no se cumple que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/math».

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>a1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mfenced><mrow><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn></mrow></mfenced><mo>/</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi></mtd></mtr><mtr><mtd><mo>(</mo><mi>g</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>=</mo><mi>b1</mi><mo>∧</mo><mo> </mo><mi>g</mi><mo>'</mo><mo>(</mo><mi>a1</mi><mo>)</mo><mo>=</mo><mi>c1</mi><mo>)</mo><mo>?</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Algunas</mi><mo> </mo><mi>posibles</mi><mo> </mo><mi>respuestas</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>k</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>k1</mi><mo>=</mo><mi>k</mi><mo>*</mo><msup><mi>a1</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mfrac><mrow><mi>k1</mi><mo>+</mo><mi>a1</mi><mo>*</mo><mi>c1</mi><mo>-</mo><mi>b1</mi></mrow><msup><mi>a1</mi><mn>2</mn></msup></mfrac></mtd></mtr><mtr><mtd><mi>t2</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>k1</mi><mo>-</mo><mi>a1</mi><mo>*</mo><mi>c1</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>b1</mi></mrow><mi>a1</mi></mfrac></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>-</mo><mi>c1</mi><mo>*</mo><mi>a1</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>t1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>t2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mo>-</mo><mi>c1</mi><mo>*</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>+</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>f1</mi><mo>,</mo><mi>f2</mi><mo>,</mo><mi>f3</mi><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Funciones</mi><mo> </mo><mi>de</mi><mo> </mo><mi>calificación</mi><mo> </mo><mi>para</mi><mo> </mo><mi>respuestas</mi><mo> </mo><mi>incompletas</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test1</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi></mtd></mtr><mtr><mtd><mo>(</mo><mi>g</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>=</mo><mi>b1</mi><mo>)</mo><mo>?</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test2</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi></mtd></mtr><mtr><mtd><mo>(</mo><mi>g</mi><mo>'</mo><mo>(</mo><mi>a1</mi><mo>)</mo><mo>=</mo><mi>c1</mi><mo>)</mo><mo>?</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>28</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>'</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>c1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>-</mo><mi>c1</mi><mo>*</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>(</mo><mn>0</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resolver</mi><mfenced><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>u</mi><mn>2</mn></msup><mo>*</mo><mi>a</mi><mo>+</mo><mi>u</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>v</mi></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mi>u</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>=</mo><mi>w</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>}</mo></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mi>u</mi><mo>*</mo><mi>w</mi><mo>-</mo><mi>v</mi></mrow><msup><mi>u</mi><mn>2</mn></msup></mfrac><mo>,</mo><mi>b</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>-</mo><mi>u</mi><mo>*</mo><mi>w</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>v</mi></mrow><mi>u</mi></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1">#sol2</correctAnswer><correctAnswer id="2">#sol3</correctAnswer></correctAnswers><assertions><assertion name="equivalent_function" correctAnswer="2"><param name="name">test2</param><param name="notevaluate">false</param></assertion><assertion name="equivalent_function" correctAnswer="1"><param name="name">test1</param><param name="notevaluate">false</param></assertion><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">fun</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 2 Dada dos condiciones sobre derivadas, determinar función que las cumplen Encuentre una función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«/math» de modo que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»`«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»`«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/math».

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«/math»

]]> 1.0000000 1.0000000 0 0 #sol Muy bien, ¡excelente respuesta!

]]> #sol2 La función que ingresaste sólo satisface la primera condición, es decir, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»`«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/math» pero no se cumple que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»F«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»`«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/math».

f(x)=#f

]]> 1.0000000 0.1000000 0 0 #sol <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>one</mi><mfenced><mrow/></mfenced><mo> </mo><mo>:</mo><mo>=</mo></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><msup><exponentiale/><mrow><mi>x</mi><mo>-</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow></msup></mtd></mtr><mtr><mtd><mi>f2</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>ln</mi><mo>(</mo><mi>x</mi><mo>-</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msup></mtd></mtr><mtr><mtd><mi>f3</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo><mo>+</mo><mn>1</mn></mtd></mtr></mtable><mrow><mi>grado</mi><mo>(</mo><mi>f3</mi><mo>)</mo><mo>&ges;</mo><mn>1</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>f4</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><msqrt><mrow><mi>x</mi><mo>-</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow></msqrt></mtd></mtr><mtr><mtd><mi>L</mi><mo>=</mo><mo>{</mo><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>f2</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>f3</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>f4</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol 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definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mrow><mrow><mi>c</mi><mo>≠</mo><mi>a</mi></mrow></apply></mtd></mtr><mtr><mtd><mi>j</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>a</mi></msub></mtd></mtr><mtr><mtd><mi>k</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>b</mi></msub></mtd></mtr><mtr><mtd><mi>l</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>composición</mi><mo>(</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mi>L</mi><mi>c</mi></msub><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mfrac><mrow><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msub><mi>L</mi><mi>c</mi></msub></mfrac></apply></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mrow><mrow><mi>c</mi><mo>≠</mo><mi>a</mi></mrow></apply></mtd></mtr><mtr><mtd><mi>j</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>a</mi></msub></mtd></mtr><mtr><mtd><mi>k</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>b</mi></msub></mtd></mtr><mtr><mtd><mi>l</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>composición</mi><mo>(</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mi>L</mi><mi>c</mi></msub><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><msub><mi>L</mi><mi>c</mi></msub><mo>)</mo></mrow></apply></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mrow><mrow><mi>c</mi><mo>≠</mo><mi>a</mi></mrow></apply></mtd></mtr><mtr><mtd><mi>j</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>a</mi></msub></mtd></mtr><mtr><mtd><mi>k</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>b</mi></msub></mtd></mtr><mtr><mtd><mi>l</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mi>L</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>composición</mi><mo>(</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>composición</mi><mo>(</mo><mi>l</mi><mo>,</mo><mi>h</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow></apply></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>one</mi><mfenced><mrow/></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>,</mo><mi>ln</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>,</mo><msqrt><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>j</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>k</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msqrt><mrow><mi>ln</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>1</mn></mrow></msqrt></mfenced><mo>*</mo><mfenced><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mi>ln</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mfenced><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><msqrt><mrow><mi>ln</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>1000</mn></mrow><mrow><mi>one</mi><mfenced><mrow/></mfenced></mrow></apply></math></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.1 Derivada de un polinomio. Dada la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mrow»«mi»#n1«/mi»«/mrow»«/msup»«mi»#s1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#s2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#s3«/mi»«mi»#n4«/mi»«/math».

Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

]]> Solución:

Para resolver, aplicamos álgebra de derivadas. En particular, ocuparemos las siguientes propiedades:

(1)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»a«/mi»«mo»·«/mo»«msup»«mi»#x«/mi»«mi»n«/mi»«/msup»«/mrow»«/mfenced»«mo»=«/mo»«mi»a«/mi»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«msup»«mi»#x«/mi»«mi»n«/mi»«/msup»«/mrow»«/mfenced»«mo»=«/mo»«mi»a«/mi»«mo»·«/mo»«mi»n«/mi»«mo»·«/mo»«msup»«mi»#x«/mi»«mrow»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§#8704;«/mo»«mi»#x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mo»§#8704;«/mo»«mi»n«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»o«/mi»«mi»n«/mi»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»a«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»

(2)

Así, aplicando la propiedad (1) tenemos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mi»#n1«/mi»«/msup»«mi»#s1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#s2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#s3«/mi»«mi»#n4«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mi»#n1«/mi»«/msup»«mo»)«/mo»«mo»§nbsp;«/mo»«mi»#s4«/mi»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#a4«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mo»)«/mo»«mo»§nbsp;«/mo»«mi»#s5«/mi»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#a5«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mo»)«/mo»«mo»§nbsp;«/mo»«mi»#s6«/mi»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»#a6«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«/math»

Luego, aplicando la propiedad (2) tenemos:

Reduciendo, obtenemos finalmente:

Por lo tanto:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#b1«/mi»«msup»«mi»#x«/mi»«mi»#n5«/mi»«/msup»«mi»#s1«/mi»«mi»#b2«/mi»«msup»«mi»#x«/mi»«mi»#n6«/mi»«/msup»«mi»#s2«/mi»«mi»#b3«/mi»«msup»«mi»#x«/mi»«mi»#n7«/mi»«/msup»«/math»

]]> 1.0000000 1.0000000 0 0 #sol Bien. Continúa de esa manera.]]> #sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>p</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cero</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>n1</mi><mo>≠</mo><mi>n2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow><mrow><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n4</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow><mrow><mi>s3</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>a4</mi><mo>=</mo><mi>a2</mi></mrow><mrow><mi>a4</mi><mo>=</mo><mo>-</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s4</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s4</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>a5</mi><mo>=</mo><mi>a3</mi></mrow><mrow><mi>a5</mi><mo>=</mo><mo>-</mo><mi>a3</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s5</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s5</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n4</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>a6</mi><mo>=</mo><mi>n4</mi></mrow><mrow><mi>a6</mi><mo>=</mo><mo>-</mo><mi>n4</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n4</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s6</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s6</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n4</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s7</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s7</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>n1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mi>n3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi><mo>=</mo><mi>n1</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n6</mi><mo>=</mo><mi>n2</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n7</mi><mo>=</mo><mi>n3</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n7</mi><mo>==</mo><mn>1</mn></mrow><mrow><mi>n7</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>n1</mi></msup><mo>+</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>n2</mi></msup><mo>+</mo><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mi>n3</mi></msup><mo>+</mo><mi>n4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mi>q</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>10</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>8</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>*</mo><msup><mi>x</mi><mn>9</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>7</mn></msup><mo>-</mo><mn>21</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol </correctAnswer><correctAnswer type="mathml"> #sol2 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.1 Derivada de un polinomio. (EVALUACIÓN) Dada la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mrow»«mi»#n1«/mi»«/mrow»«/msup»«mi»#s1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#s2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#s3«/mi»«mi»#n4«/mi»«/math».

Entonces, #X

#gr

]]> Solución:

Para resolver, primero debemos obtener «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«/math». Para ello ocuparemos las siguientes propiedades:

(1)

(2)

Así, aplicando la propiedad (1) tenemos:

Luego, aplicando la propiedad (2) tenemos:

Reduciendo, obtenemos finalmente:

Por lo tanto:

Ahora, debemos evaluar el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#x«/mi»«mo»=«/mo»«mi»#x1«/mi»«/math» en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«/math», es decir:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»#x1«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#b1«/mi»«mo»(«/mo»«mi»#x1«/mi»«msup»«mo»)«/mo»«mi»#n5«/mi»«/msup»«mi»#s1«/mi»«mi»#b2«/mi»«mo»(«/mo»«mi»#x1«/mi»«msup»«mo»)«/mo»«mi»#n6«/mi»«/msup»«mi»#s2«/mi»«mi»#b3«/mi»«mo»(«/mo»«mi»#x1«/mi»«msup»«mo»)«/mo»«mi»#n7«/mi»«/msup»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»#x1«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#b1«/mi»«mo»(«/mo»«mi»#e1«/mi»«mo»)«/mo»«mi»#s1«/mi»«mi»#b2«/mi»«mo»(«/mo»«mi»#e2«/mi»«mo»)«/mo»«mi»#s2«/mi»«mi»#b3«/mi»«mo»(«/mo»«mi»#e3«/mi»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

Luego, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»#x1«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#sol9«/mi»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

Pregunta abierta:

¿Qué significa que #X«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#sol9«/mi»«/math»?

]]> 1.0000000 1.0000000 0 0 #sol9 Bien. Continúa de esa manera.]]> #sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>p</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cero</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>n1</mi><mo>≠</mo><mi>n2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>n1</mi></msup><mo>+</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>n2</mi></msup><mo>+</mo><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mi>n3</mi></msup><mo>+</mo><mi>n4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow><mrow><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n4</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow><mrow><mi>s3</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>a4</mi><mo>=</mo><mi>a2</mi></mrow><mrow><mi>a4</mi><mo>=</mo><mo>-</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s4</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s4</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>a5</mi><mo>=</mo><mi>a3</mi></mrow><mrow><mi>a5</mi><mo>=</mo><mo>-</mo><mi>a3</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s5</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s5</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n4</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>a6</mi><mo>=</mo><mi>n4</mi></mrow><mrow><mi>a6</mi><mo>=</mo><mo>-</mo><mi>n4</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n4</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s6</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s6</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n4</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s7</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s7</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>n1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mi>n3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi><mo>=</mo><mi>n1</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n6</mi><mo>=</mo><mi>n2</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n7</mi><mo>=</mo><mi>n3</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n7</mi><mo>==</mo><mn>1</mn></mrow><mrow><mi>n7</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>n1</mi></msup><mo>+</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>n2</mi></msup><mo>+</mo><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mi>n3</mi></msup><mo>+</mo><mi>n4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><msup><mi>x1</mi><mi>n5</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><msup><mi>x1</mi><mi>n6</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n7</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>e3</mi><mo>=</mo><mi>x1</mi></mrow><mrow><mi>e3</mi><mo>=</mo><msup><mi>x1</mi><mi>n7</mi></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>e1</mi><mo>*</mo><mi>b1</mi><mo>+</mo><mi>e2</mi><mo>*</mo><mi>b2</mi><mo>+</mo><msup><mi>x1</mi><mi>n7</mi></msup><mo>*</mo><mi>b3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol9</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi><mo>=</mo><mi>x1</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>&quot;</mo><mi>es</mi><mo> </mo><mi>igual</mi><mo> </mo><mi>a</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>vale</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><apply><diff/><bvar><mrow><mo>#</mo><mn>2</mn></mrow></bvar><mrow><mi>f</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo></mrow></apply><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>pendiente</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>tangente</mi><mo> </mo><mi>a</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>al</mi><mo> </mo><mi>evaluar</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>X1</mi><mo>,</mo><mi>X2</mi><mo>,</mo><mi>X3</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>centro</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo><mo>,</mo><mi>anchura</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>1000</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gr</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mfenced><mrow><mi>t1</mi><mo>,</mo><mi>punto</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>azul</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>f1</mi><mo>&apos;</mo><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol9</mi><mo>=</mo><mi>f2</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>9</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>81</mn><mo>*</mo><msup><mi>y</mi><mn>8</mn></msup><mo>+</mo><mn>40</mn><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>20128</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol9</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>20128</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e111</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e111</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>31</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol9 </correctAnswer><correctAnswer type="mathml"> #sol2 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.2 Derivada de una suma de raíces. Sea la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f«/mi»«mo»(«/mo»«mi»#k«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«/math».

Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«mfenced»«mrow»«mi»#k«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#k«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

]]> Solución:

Para resolver, aplicamos álgebra de derivadas. En este caso, haremos uso de las siguientes propiedades:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»p«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/mfenced»«mo»±«/mo»«mi»q«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»p«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»±«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»q«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«/math»
(1)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«msup»«mi»#x«/mi»«mi»m«/mi»«/msup»«/mfenced»«mo»=«/mo»«mi»m«/mi»«mo»·«/mo»«msup»«mi»#x«/mi»«mrow»«mi»m«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«/mtable»«/math»
(2)

Aplicando la propiedad (1) se obtiene:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mo»)«/mo»«mi»#s2«/mi»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n22«/mi»«mi»#r2«/mi»«mo»)«/mo»«/math»

Escribiendo cada raíz en forma de potencia se obtiene:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«msup»«mi»#x«/mi»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«/msup»«mo»)«/mo»«mi»#s2«/mi»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n22«/mi»«msup»«mi»#x«/mi»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«/msup»«mo»)«/mo»«/math»

Aplicando la propiedad (2):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#n1«/mi»«mo»·«/mo»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«msup»«mi»#x«/mi»«mrow»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mi»#s1«/mi»«mi»#n2«/mi»«mo»·«/mo»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«msup»«mi»#x«/mi»«mrow»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»

Reduciendo:

Reescribiendo como raíz se tiene:

]]> 1.0000000 1.0000000 0 0 #sol ¡Muy bien! Sigue así.]]> #sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

Entonces, #X

#gr

Obs.: Puede ingresar la respuesta exacta o aproximada, considerando 2 decimales de precisión

]]> Solución:

Para resolver, primero debemos obtener «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«/math».

En este caso, haremos uso de las siguientes propiedades:

Aplicando la propiedad (1) se obtiene:

Escribiendo cada raíz en forma de potencia se obtiene:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«msup»«mi»#x«/mi»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«/msup»«mo»)«/mo»«mi»#s2«/mi»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n22«/mi»«msup»«mi»#x«/mi»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«/msup»«mo»)«/mo»«/math»

Aplicando la propiedad (2):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#n1«/mi»«mo»·«/mo»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«msup»«mi»#x«/mi»«mrow»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mi»#s1«/mi»«mi»#n2«/mi»«mo»·«/mo»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«msup»«mi»#x«/mi»«mrow»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»

Reduciendo:

Reescribiendo como raíz se tiene:

Luego, evaluamos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#x1«/mi»«/math» en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«/math», es decir:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«mo»(«/mo»«mi»#x1«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mi»#n3«/mi»«mfrac»«mn»1«/mn»«mroot»«msup»«mi»#x1«/mi»«mi»#nu«/mi»«/msup»«mi»#de«/mi»«/mroot»«/mfrac»«mi»#s1«/mi»«mi»#n4«/mi»«mfrac»«mn»1«/mn»«mroot»«msup»«mi»#x1«/mi»«mi»#nu1«/mi»«/msup»«mi»#de2«/mi»«/mroot»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

Desarrollando, obtenemos:

Por lo tanto, #X «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#sol1«/mi»«mo»§#8776;«/mo»«mi»#sol3«/mi»«/math»

Pregunta abierta:

¿Qué significa que #X «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8776;«/mo»«mi»#sol3«/mi»«/math»?

]]> 1.0000000 1.0000000 0 0 #sol1 ¡Muy bien! Sigue así.]]> #sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

]]> #sol3 ¡Muy bien! Sigue así.]]> #sol4 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>m</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>p</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mroot><msup><mi>x</mi><mi>e1</mi></msup><mi>i1</mi></mroot></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>e1</mi><mo>&lt;</mo><mi>i1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mroot><msup><mi>x</mi><mi>e2</mi></msup><mi>i2</mi></mroot></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>e2</mi><mo>&lt;</mo><mi>i2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>n22</mi><mo>=</mo><mi>n2</mi></mrow><mrow><mi>n22</mi><mo>=</mo><mo>-</mo><mi>n2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mfrac><mrow><mi>n1</mi><mo>*</mo><mi>e1</mi></mrow><mi>i1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mfrac><mrow><mi>n2</mi><mo>*</mo><mi>e2</mi></mrow><mi>i2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mo>(</mo><mi>e1</mi><mo>/</mo><mi>i1</mi><mo>)</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi><mo>=</mo><mo>(</mo><mi>e2</mi><mo>/</mo><mi>i2</mi><mo>)</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nu</mi><mo>=</mo><mo>-</mo><mi>numerador</mi><mo>(</mo><mi>e3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mi>denominador</mi><mo>(</mo><mi>e3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nu1</mi><mo>=</mo><mo>-</mo><mi>numerador</mi><mo>(</mo><mi>e4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de2</mi><mo>=</mo><mi>denominador</mi><mo>(</mo><mi>e4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><msup><mi>x</mi><mi>e3</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msup><mi>x</mi><mi>e4</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>n1</mi><mo>*</mo><mroot><msup><mi>x</mi><mi>e1</mi></msup><mi>i1</mi></mroot><mo>+</mo><mi>n2</mi><mo>*</mo><mroot><msup><mi>x</mi><mi>e2</mi></msup><mi>i2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mo>(</mo><mi>n1</mi><mo>*</mo><mi>r1</mi><mo>+</mo><mi>n2</mi><mo>*</mo><mi>r2</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f1</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi><mo>=</mo><mi>x1</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>&quot;</mo><mi>es</mi><mo> </mo><mi>igual</mi><mo> </mo><mi>a</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>vale</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><apply><diff/><bvar><mrow><mo>#</mo><mn>2</mn></mrow></bvar><mrow><mi>f</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo></mrow></apply><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>pendiente</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>tangente</mi><mo> </mo><mi>a</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>al</mi><mo> </mo><mi>evaluar</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>X1</mi><mo>,</mo><mi>X2</mi><mo>,</mo><mi>X3</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>f1</mi><mo>&apos;</mo><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>f2</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>a_decimal</mi><mo>(</mo><mo>(</mo><mi>redondear</mi><mo>(</mo><mi>sol1</mi><mo>*</mo><mn>100</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inf</mi><mo>=</mo><mi>a_decimal</mi><mo>(</mo><mo>(</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>sol1</mi><mo>*</mo><mn>10</mn><mo>)</mo></mrow></mfenced><mo>/</mo><mn>10</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sup</mi><mo>=</mo><mi>a_decimal</mi><mo>(</mo><mo>(</mo><mfenced close="⌉" open="⌈"><mrow><mo>(</mo><mi>sol1</mi><mo>*</mo><mn>10</mn><mo>)</mo></mrow></mfenced><mo>/</mo><mn>10</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>&ges;</mo><mi>inf</mi><mo>∧</mo><mi>x</mi><mo>&les;</mo><mi>sup</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol3</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>centro</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>anchura</mi><mo>=</mo><mn>14</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>100</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gr</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>punto</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mroot><mn>2</mn><mn>3</mn></mroot><mn>3</mn></mfrac><mo>+</mo><mfrac><mrow><mn>10</mn><mo>*</mo><mroot><mn>16</mn><mn>7</mn></mroot></mrow><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.54</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mroot><msup><mi>p</mi><mn>4</mn></msup><mn>7</mn></mroot><mo>+</mo><mn>2</mn><mo>*</mo><mroot><msup><mi>p</mi><mn>2</mn></msup><mn>6</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>20</mn><mo>*</mo><mroot><msup><mi>p</mi><mn>4</mn></msup><mn>7</mn></mroot></mrow><mrow><mn>7</mn><mo>*</mo><mi>p</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mroot><msup><mi>p</mi><mn>2</mn></msup><mn>6</mn></mroot></mrow><mrow><mn>3</mn><mo>*</mo><mi>p</mi></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mroot><mn>2</mn><mn>3</mn></mroot><mo>+</mo><mn>5</mn><mo>*</mo><mroot><mn>16</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mroot><mn>2</mn><mn>3</mn></mroot><mn>3</mn></mfrac><mo>+</mo><mfrac><mrow><mn>10</mn><mo>*</mo><mroot><mn>16</mn><mn>7</mn></mroot></mrow><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>num</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>numerador</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol1 </correctAnswer><correctAnswer type="mathml"> #sol2 </correctAnswer><correctAnswer type="mathml"> #sol3 </correctAnswer><correctAnswer type="mathml"> #sol4 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="syntax_expression" correctAnswer="2"/><assertion name="syntax_expression" correctAnswer="3"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion><assertion name="equivalent_function" correctAnswer="3"><param name="name">test1</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.3 Derivada de una suma de trigonométricas. Sea la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mo»=«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«/math».

Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#a«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

Obs.:

1. La función seno de x se ingresa: sen(x)

2. La función coseno de x se ingresa: cos(x)

3. La función tangente de x se ingresa: tan(x)

]]> Solución:

Para calcular la derivada de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mo»=«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«/math» , aplicaremos álgebra de derivadas. En particular, ocuparemos las siguientes propiedades:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»A«/mi»«mo»·«/mo»«mi»p«/mi»«mfenced»«mi»#w«/mi»«/mfenced»«mo»±«/mo»«mi»B«/mi»«mo»·«/mo»«mi»q«/mi»«mfenced»«mi»#w«/mi»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mi»A«/mi»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»p«/mi»«mfenced»«mi»#w«/mi»«/mfenced»«/mrow»«/mfenced»«mo»±«/mo»«mi»B«/mi»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»q«/mi»«mfenced»«mi»#w«/mi»«/mfenced»«/mrow»«/mfenced»«/math»
(1)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mfrac»«mrow»«mi»p«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»q«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»p«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»·«/mo»«mi»q«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»-«/mo»«mi»p«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»q«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi»q«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math» (2)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mo»-«/mo»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/math»
(3)

Cálculo de la derivada de la Tangente.
Antes de abordar el problema del cálculo de la derivada de la suma de funciones trigonométricas, primero realizaremos el cálculo de la derivada de la función tangente.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«/math»

/ Ocupando la identidad «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math» tenemos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mfrac»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«/math»

/ Ocupando (2),tenemos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»·«/mo»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»-«/mo»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mo»=«/mo»«/math»

/ Ocupando la propiedad (3) enunciada al inicio de la resolución, tenemos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»-«/mo»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mo»-«/mo»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mo»=«/mo»«/math»

/ Desarrollando los productos del numerador:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»sen«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«/math»

/ Separando en suma de dos fracciones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«menclose notation=¨updiagonalstrike¨»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/menclose»«menclose notation=¨updiagonalstrike¨»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/menclose»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»s«/mi»«mi»e«/mi»«msup»«mi»n«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«/math»

/ Ocupando «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math», se obtiene finalmente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»tan«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/math»

Por lo tanto,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»tan«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/math» (4)

Cálculo de la derivada de la suma de funciones trigonométricas.
Abordaremos ahora el problema de la derivada de la suma de las funciones trigonométricas.
Ocupando la propiedad (1) obtenemos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«mo»)«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mi»#n1«/mi»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»#t1«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mi»#s1«/mi»«mi»#n2«/mi»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»#t2«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«/math»

Ocupando las propiedades (3) y (4) obtenemos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«mo»)«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mi»#n1«/mi»«mo»(«/mo»«mi»#d1«/mi»«mo»)«/mo»«mi»#s1«/mi»«mi»#n2«/mi»«mfenced»«mrow»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»tan«/mi»«mn»2«/mn»«/msup»«mfenced»«mi»#w«/mi»«/mfenced»«/mrow»«/mfenced»«/math»

Por último, reduciendo términos nos queda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mi»#sol«/mi»«/math»

Por lo tanto:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#a«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#sol«/mi»«/math»

]]> 1.0000000 1.0000000 0 0 #sol ¡Excelente!]]> #sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>n2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>s</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>t11</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sen</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>t22</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>tan</mi><mo>(</mo><mi>w</mi><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a11</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>t11</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>t22</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><apply><diff/><bvar><mi>w</mi></bvar><mi>t1</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><diff/><bvar><mi>w</mi></bvar><mrow><mo>(</mo><mi>n1</mi><mo>*</mo><mi>t1</mi><mo>+</mo><mi>n3</mi><mo>*</mo><mi>t2</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mi>y</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>y</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><diff/><bvar><mi>w</mi></bvar><mi>t1</mi></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>sen</mi><mfenced><mi>y</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mi>y</mi></mfenced></math></output></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol </correctAnswer><correctAnswer type="mathml"> #sol2 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.3 Extendida Derivada de una suma de trigonométricas. (EVALUACIÓN) Sea la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mo»=«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«/math».

Entonces, #X

#gr

Obs.:

1. La función seno de x se ingresa: sen(x)

2. La función coseno de x se ingresa: cos(x)

3. La función tangente de x se ingresa: tan(x)

4. Puede ingresar la respuesta exacta o aproximada, considerando 2 decimales de precisión.

]]> Solución:

Primero debemos obtener la derivada de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mo»=«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«/math» .

Ocuparemos las siguientes propiedades:

Cálculo de la derivada de la suma de funciones trigonométricas.
Abordaremos ahora el problema de la derivada de la suma de las funciones trigonométricas.
Ocupando la propiedad (1) obtenemos:

Ocupando las propiedades (3) y (4) obtenemos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«mo»)«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mi»#n1«/mi»«mo»(«/mo»«mi»#d1«/mi»«mo»)«/mo»«mi»#s1«/mi»«mi»#n2«/mi»«mfenced»«mrow»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»tan«/mi»«mn»2«/mn»«/msup»«mfenced»«mi»#w«/mi»«/mfenced»«/mrow»«/mfenced»«/math»

Por último, reduciendo términos nos queda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mi»#sol«/mi»«/math»

Por lo tanto:

Luego, evaluando «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#w«/mi»«mo»=«/mo»«mi»#x1«/mi»«/math» en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#a«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«/math» obtenemos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#sol2«/mi»«mo»§#8776;«/mo»«mi»#sol3«/mi»«/math».

Por lo tanto #X «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#sol2«/mi»«mo»§#8776;«/mo»«mi»#sol3«/mi»«/math»

Pregunta abierta:

¿Qué significa que #X«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8776;«/mo»«mi»#sol3«/mi»«mo»?«/mo»«/math»

]]> 1.0000000 1.0000000 0 0 #sol2 ¡Excelente!]]> #sol4 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> #sol3 ¡Excelente!]]> #sol5 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mfrac><pi/><mn>4</mn></mfrac><mo>,</mo><mfrac><pi/><mn>3</mn></mfrac><mo>,</mo><mfrac><pi/><mn>6</mn></mfrac><mo>,</mo><mfrac><mrow><mn>5</mn><pi/></mrow><mn>6</mn></mfrac><mo>,</mo><mfrac><mrow><mn>3</mn><pi/></mrow><mn>4</mn></mfrac><mo>,</mo><mfrac><mrow><mn>2</mn><pi/></mrow><mn>3</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>n2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>s</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>t11</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sen</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>t22</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>tan</mi><mo>(</mo><mi>w</mi><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a11</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>t11</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>t22</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>n1</mi><mo>*</mo><mi>t11</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>+</mo><mi>n2</mi><mo>*</mo><mi>t22</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>f1</mi><mo>&apos;</mo><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>f2</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>f1</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><apply><diff/><bvar><mi>w</mi></bvar><mi>t1</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><apply><diff/><bvar><mi>w</mi></bvar><mi>t2</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><diff/><bvar><mi>w</mi></bvar><mrow><mo>(</mo><mi>n1</mi><mo>*</mo><mi>t1</mi><mo>+</mo><mi>n3</mi><mo>*</mo><mi>t2</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>a_decimal</mi><mo>(</mo><mo>(</mo><mi>redondear</mi><mo>(</mo><mi>sol2</mi><mo>*</mo><mn>100</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inf</mi><mo>=</mo><mi>a_decimal</mi><mo>(</mo><mo>(</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>sol2</mi><mo>*</mo><mn>10</mn><mo>)</mo></mrow></mfenced><mo>/</mo><mn>10</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sup</mi><mo>=</mo><mi>a_decimal</mi><mo>(</mo><mo>(</mo><mfenced close="⌉" open="⌈"><mrow><mo>(</mo><mi>sol2</mi><mo>*</mo><mn>10</mn><mo>)</mo></mrow></mfenced><mo>/</mo><mn>10</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>&ges;</mo><mi>inf</mi><mo>∧</mo><mi>x</mi><mo>&les;</mo><mi>sup</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol2</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>w</mi><mo>=</mo><mi>x1</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>&quot;</mo><mi>es</mi><mo> </mo><mi>igual</mi><mo> </mo><mi>a</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>vale</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>pendiente</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>tangente</mi><mo> </mo><mi>a</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>al</mi><mo> </mo><mi>evaluar</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>X1</mi><mo>,</mo><mi>X3</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Tablero</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>centro</mi><mo>=</mo><mi>P</mi><mo>,</mo><mi>anchura</mi><mo>=</mo><mn>8</mn><pi/><mo>,</mo><mi>altura</mi><mo>=</mo><mn>8</mn><pi/><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>t3</mi><mo>,</mo><mi>punto</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gr</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t3</mi><mo>,</mo><mi>f1</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><pi/></mrow><mn>6</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>tan</mi><msup><mfenced><mi>y</mi></mfenced><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>sen</mi><mfenced><mi>y</mi></mfenced><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mfrac><mn>8</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mfrac><mn>8</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><pi/></mrow><mn>6</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6.13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol2 </correctAnswer><correctAnswer type="mathml"> #sol4 </correctAnswer><correctAnswer type="mathml"> #sol3 </correctAnswer><correctAnswer type="mathml"> #sol5 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="syntax_expression" correctAnswer="2"/><assertion name="syntax_expression" correctAnswer="3"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion><assertion name="equivalent_function" correctAnswer="3"><param name="name">test1</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.4 Derivada de la suma de exponencial y logaritmo. Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»#a«/mi»«msup»«mi»#e«/mi»«mrow»«mi»#v«/mi»«/mrow»«/msup»«mi»#c«/mi»«mi»#b«/mi»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math». Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#v«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

]]> Solución:

Recuerda que en álgebra de derivadas, la derivada de la #s de dos funciones es la #s de las derivadas de cada una de ellas; por esto separaremos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math» de la siguiente forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mi»g«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«mi»#c1«/mi»«mi»#h«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/math»

Donde:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mi»g«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mi»#a«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mi»h«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mi»#k«/mi»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«/mtr»«/mtable»«/math»

Así, la derivada de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math» es:

Ahora, procedamos a calcular las derivadas correspondientes.

Así:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mtable»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»g«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»#a«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mrow»«/mfenced»«mo»=«/mo»«mi»#a«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mtd»«/mtr»«/mtable»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math», ya que la derivada de la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»e«/mi»«mrow»«mi»#v«/mi»«/mrow»«/msup»«/math» es la misma función.

Ahora derivamos la segunda función:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»h«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi mathvariant=¨normal¨»#k#ln«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»#k«/mi»«mi»#v«/mi»«/mfrac»«/mtd»«/mtr»«/mtable»«/math», ya que la derivada de la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math» es «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mi»#v«/mi»«/mrow»«/mfrac»«/math».

Por lo tanto,

]]> 1.0000000 1.0000000 0 0 #sol Bien. Continúa de esa manera.]]> sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>20</mn></mrow></mfenced><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>20</mn></mrow></mfenced><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>c</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mrow><mrow><mi>c</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s</mi><mo>=</mo><mo>&quot;</mo><mi>diferencia</mi><mo>&quot;</mo></mrow><mrow><mi>s</mi><mo>=</mo><mo>&quot;</mo><mi>suma</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><exponentiale/><mi>v</mi></msup><mo>-</mo><mfrac><mi>k</mi><mi>v</mi></mfrac></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><exponentiale/><mi>v</mi></msup><mo>+</mo><mfrac><mi>k</mi><mi>v</mi></mfrac></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol </correctAnswer><correctAnswer type="mathml"> sol2 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.5 Derivada de la multiplicación entre un polinomio y una trigonométrica. Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mi»#t«/mi»«mo»·«/mo»«mfenced»«mrow»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mrow»«mi»#n1«/mi»«/mrow»«/msup»«mi»#c1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mrow»«mi»#n2«/mi»«/mrow»«/msup»«mi»#c2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mrow»«mi»#n3«/mi»«/mrow»«/msup»«mi»#c3«/mi»«mi»#a4«/mi»«/mrow»«/mfenced»«/math».

Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

Obs.:

Ingresa las funciones trigonométricas de la siguiente manera:

1. seno(x) se ingresa sen(x)

2. coseno(x) se ingresa cos(x)

3. tangente(x) se ingresa tan(x)

4. cosecante(x) se ingresa cosec(x)

5. secante(x) se ingresa sec(x)

6. cotangente(x) se ingresa cotan(x)

]]> Solución:

Recuerda que la derivada de la multiplicación de dos funciones se desarrolla de la siguiente manera:

Si:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»·«/mo»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»

Entonces, la derivada de la multiplicación de estas dos funciones es:

Con lo anterior, se puede escribir «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mi»#t«/mi»«mo»·«/mo»«mfenced»«mrow»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mi»#n1«/mi»«/msup»«mi»#c1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#c2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#c3«/mi»«mi»#a4«/mi»«/mrow»«/mfenced»«/math» de la siguiente forma:

En nuestro caso:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable»«mtr»«mtd»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#t«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mi»#n1«/mi»«/msup»«mi»#c1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#c2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#c3«/mi»«mi»#a4«/mi»«/mtd»«/mtr»«/mtable»«/math»

Donde «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» es un polinomio.

Así,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfenced»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»#t«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mfenced»«mrow»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mi»#n1«/mi»«/msup»«mi»#c1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#c2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#c3«/mi»«mi»#a4«/mi»«/mrow»«/mfenced»«mo»+«/mo»«mi»#t«/mi»«mo»·«/mo»«mfenced»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mi»#n1«/mi»«/msup»«mi»#c1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#c2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#c3«/mi»«mi»#a4«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«/math»

Ahora procedemos a derivar las funciones anteriores

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»#t«/mi»«mo»=«/mo»«mi»#t1«/mi»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mtable»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mi»#n1«/mi»«/msup»«mi»#c1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#c2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#c3«/mi»«mi»#a4«/mi»«/mrow»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»#n1«/mi»«msup»«mi»#x«/mi»«mrow»«mi»#n1«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mi»#c1«/mi»«mi»#a2«/mi»«mo»·«/mo»«mi»#n2«/mi»«msup»«mi»#x«/mi»«mrow»«mi»#n2«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mi»#c2«/mi»«mi»#a3«/mi»«mo»·«/mo»«mi»#n3«/mi»«msup»«mi»#x«/mi»«mrow»«mi»#n3«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#r1«/mi»«msup»«mi»#x«/mi»«mi»#r2«/mi»«/msup»«mi»#c1«/mi»«mi»#r3«/mi»«msup»«mi»#x«/mi»«mi»#r4«/mi»«/msup»«mi»#c2«/mi»«mi»#r5«/mi»«msup»«mi»#x«/mi»«mi»#r6«/mi»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«/mtable»«/mtd»«/mtr»«/mtable»«/math»

Por lo tanto,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mi»#t2«/mi»«mo»·«/mo»«mfenced»«mrow»«mi»#a1«/mi»«msup»«mi»#x«/mi»«mi»#n1«/mi»«/msup»«mi»#c1«/mi»«mi»#a2«/mi»«msup»«mi»#x«/mi»«mi»#n2«/mi»«/msup»«mi»#c2«/mi»«mi»#a3«/mi»«msup»«mi»#x«/mi»«mi»#n3«/mi»«/msup»«mi»#c3«/mi»«mi»#a4«/mi»«/mrow»«/mfenced»«mo»+«/mo»«mi»#t«/mi»«mo»·«/mo»«mfenced»«mrow»«mi»#r1«/mi»«msup»«mi»#x«/mi»«mi»#r2«/mi»«/msup»«mi»#c1«/mi»«mi»#r3«/mi»«msup»«mi»#x«/mi»«mi»#r4«/mi»«/msup»«mi»#c2«/mi»«mi»#r5«/mi»«msup»«mi»#x«/mi»«mi»#r6«/mi»«/msup»«/mrow»«/mfenced»«/math»

]]> 1.0000000 1.0000000 0 0 #sol ¡Muy bien! Sigue así.]]> sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>sen</mi><mfenced><mi>x</mi></mfenced><mo>,</mo><mi>cos</mi><mfenced><mi>x</mi></mfenced><mo>,</mo><mi>tan</mi><mfenced><mi>x</mi></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>20</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>20</mn></mrow></mfenced><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>20</mn></mrow></mfenced><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>20</mn></mrow></mfenced><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>5</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>5</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>5</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr></mtable><mrow><mi>n3</mi><mo>&lt;</mo><mi>n2</mi><mo>∧</mo><mi>n2</mi><mo>&lt;</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mrow><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>c2</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mrow><mrow><mi>c2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a4</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>c3</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mrow><mrow><mi>c3</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>n1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>n1</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>n2</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r5</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mi>n3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r6</mi><mo>=</mo><mi>n3</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mi>t</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t</mi><mo>=</mo><mi>tan</mi><mfenced><mi>x</mi></mfenced></mrow><mrow><mi>t2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>t1</mi></mrow></mfenced></mrow><mrow><mi>t2</mi><mo>=</mo><mi>t1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mi>t1</mi></mfenced><mo>*</mo><mfenced><mrow><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>n1</mi></msup><mo>+</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>n2</mi></msup><mo>+</mo><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mi>n3</mi></msup><mo>+</mo><mi>a4</mi></mrow></mfenced><mo>+</mo><mi>t</mi><mo>*</mo><mfenced><mrow><mi>r1</mi><mo>*</mo><msup><mi>x</mi><mi>r2</mi></msup><mo>+</mo><mi>r3</mi><mo>*</mo><msup><mi>x</mi><mi>r4</mi></msup><mo>+</mo><mi>r5</mi><mo>*</mo><msup><mi>x</mi><mi>r6</mi></msup></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol </correctAnswer><correctAnswer type="mathml"> sol2 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.6 Derivada de la multiplicación entre una exponencial y una trigonométrica. Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mi»#a1«/mi»«mi»#tri«/mi»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/math». Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#v«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

Obs.:

Ingresa las funciones trigonométricas de la siguiente manera:

1. seno(x) se ingresa sen(x)

2. coseno(x) se ingresa cos(x)

]]> Solución:

Recuerda que la derivada de la multiplicación de dos funciones se desarrolla de la siguiente manera:

Si:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»g«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi»h«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math»

Entonces, la derivada de la multiplicación de estas dos funciones es:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»g«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi»h«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»+«/mo»«mi»g«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»h«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math»

Con lo anterior, se puede separar «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mi»#a1«/mi»«mi»#tri«/mi»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/math» de la siguiente forma:

Con:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable»«mtr»«mtd»«mi»g«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a1«/mi»«mi»#tri«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»h«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mtd»«/mtr»«/mtable»«/math»

Así,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mfenced»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»#a1«/mi»«mi»#tri«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«mo»+«/mo»«mi»#a1«/mi»«mi»#tri«/mi»«mo»·«/mo»«mfenced»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mrow»«/mfenced»«/mrow»«/mfenced»«/math»

Ahora procedemos a derivar las funciones anteriores:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»#a1«/mi»«mi»#tri«/mi»«mo»=«/mo»«mi»#t1«/mi»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«mo»=«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/math», ya que la derivada de la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»e«/mi»«mrow»«mi»#v«/mi»«/mrow»«/msup»«/math» es la misma función.

Por lo tanto,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mtable»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#t1«/mi»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«mo»+«/mo»«mi»#a1«/mi»«mi»#tri«/mi»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a6«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«mo»+«/mo»«mi»#a3«/mi»«mi»#tri«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mtd»«/mtr»«/mtable»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

]]> 1.0000000 1.0000000 0 0 #sol ¡Muy bien! Sigue así.]]> sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>t</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>sen</mi><mfenced><mi>v</mi></mfenced><mo>,</mo><mi>cos</mi><mfenced><mi>v</mi></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>20</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>20</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><apply><diff/><bvar><mi>v</mi></bvar><mfenced><mrow><mi>a1</mi><mo>*</mo><mi>tri</mi></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><apply><diff/><bvar><mi>v</mi></bvar><mrow><mo>(</mo><mi>tri</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>tri</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mrow><mi>a6</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>-</mo><mo>#</mo><mn>1</mn><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>a5</mi><mo>,</mo><mi>sen</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>a6</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>a5</mi><mo>,</mo><mi>t2</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>t1</mi><mo>*</mo><mi>a2</mi><mo>*</mo><msup><exponentiale/><mi>v</mi></msup><mo>+</mo><mi>a1</mi><mo>*</mo><mi>tri</mi><mo>*</mo><mi>a2</mi><mo>*</mo><msup><exponentiale/><mi>v</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sen</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>260</mn><mi>cos</mi><mfenced><mi>x</mi></mfenced><ms>#</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>15</mn><mo>*</mo><mi>sen</mi><mfenced><mi>t</mi></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a6</mi></math></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol </correctAnswer><correctAnswer type="mathml"> sol2 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.7 Derivada de la mult. entre raíz y ln. (23.7) Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f«/mi»«/math». Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»
]]> Solución:

Debemos derivar la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f«/mi»«/math», la cual corresponde a una multiplicación de funciones.

Por lo tanto, aplicaremos la regla de derivación para un producto de funciones:

Sean «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«/math» dos funciones, entonces:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»·«/mo»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»·«/mo»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»+«/mo»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/math»

Para el caso particular de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f«/mi»«/math», su derivada es:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#g«/mi»«mo»·«/mo»«mi»#h«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»/«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mo»§nbsp;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mo»§nbsp;«/mo»«mi»#g«/mi»«mo»·«/mo»«mi»#h«/mi»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#g«/mi»«/mfenced»«mo»·«/mo»«mi»#h«/mi»«mo»+«/mo»«mi»#g«/mi»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#h«/mi»«/mfenced»«/mtd»«/mtr»«/mtable»«/math»

Derivaremos cada función por separado para una mejor comprensión del problema:

Sean «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»=«/mo»«mi»#g«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»h«/mi»«mo»=«/mo»«mi»#h«/mi»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»A«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#g«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»/«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»#g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»;«/mo»«mo»§nbsp;«/mo»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mi»e«/mi»«mi»r«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mroot»«mi»#x«/mi»«mi»#n«/mi»«/mroot»«mo»=«/mo»«msup»«mi»#x«/mi»«mfrac»«mn»1«/mn»«mi»#n«/mi»«/mfrac»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«msup»«mi»#x«/mi»«mfrac»«mn»1«/mn»«mi»#n«/mi»«/mfrac»«/msup»«/mfenced»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mi»#n«/mi»«/mfrac»«mo»·«/mo»«msup»«mi»#x«/mi»«mfenced»«mrow»«mfrac»«mn»1«/mn»«mi»#n«/mi»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«msup»«mi»#x«/mi»«mfenced»«mfrac»«mrow»«mn»1«/mn»«mo»-«/mo»«mi»#n«/mi»«/mrow»«mi»#n«/mi»«/mfrac»«/mfenced»«/msup»«mi»#n«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«msup»«mi»#x«/mi»«mfrac»«mi»#e«/mi»«mi»#n«/mi»«/mfrac»«/msup»«mo»§nbsp;«/mo»«/mrow»«mi»#n«/mi»«/mfrac»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»;«/mo»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mi»e«/mi»«mi»r«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«msup»«mi»#x«/mi»«mrow»«mo»-«/mo»«mi»n«/mi»«/mrow»«/msup»«mo»=«/mo»«mfrac»«mn»1«/mn»«msup»«mi»#x«/mi»«mi»n«/mi»«/msup»«/mfrac»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mrow»«mi»#n«/mi»«mo»·«/mo»«msup»«mi»#x«/mi»«mfrac»«mi»#e1«/mi»«mi»#n«/mi»«/mfrac»«/msup»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mi»e«/mi»«mi»r«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«msup»«mi»#x«/mi»«mfrac»«mi»#e1«/mi»«mi»#n«/mi»«/mfrac»«/msup»«mo»=«/mo»«mroot»«mi»#x«/mi»«mi»#n«/mi»«/mroot»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#p1«/mi»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»p«/mi»«mi»o«/mi»«mi»r«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»o«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»tan«/mi»«mi»t«/mi»«mi»o«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mi»#p1«/mi»«/mtd»«/mtr»«/mtable»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mi»B«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mi»h«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#h«/mi»«mo»§nbsp;«/mo»«mo»/«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#h«/mi»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi»P«/mi»«mi»o«/mi»«mi»r«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»o«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»tan«/mi»«mi»t«/mi»«mi»o«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mi»#p2«/mi»«/mtd»«/mtr»«/mtable»«/math»
Finalmente, por lo realizado en A) y B) tenemos que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#p1«/mi»«mo»·«/mo»«mi»#h«/mi»«mo»+«/mo»«mi»#g«/mi»«mo»·«/mo»«mi»#p2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#sol1«/mi»«mo»+«/mo»«mi»#sol2«/mi»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#prima«/mi»«mo».«/mo»«/mtd»«/mtr»«/mtable»«/math»

]]> 1.0000000 1.0000000 0 0 #prima Bien. Continúa de esa manera.]]> #sol4 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

]]> Solución:

Debemos derivar la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»#g«/mi»«mi»#h«/mi»«/mfrac»«/math»

Observa que la función dada es un cuociente (división) de funciones, cuya forma de derivar es:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»/«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»-«/mo»«mfenced close=¨}¨ open=¨{¨»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»
Para el caso particular de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»#g«/mi»«mi»#h«/mi»«/mfrac»«/math», su derivada es:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»#g«/mi»«mi»#h«/mi»«/mfrac»«mo»§nbsp;«/mo»«mo»/«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfenced»«mi»#h«/mi»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#g«/mi»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mfenced»«mi»#g«/mi»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#h«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mi»#h«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»S«/mi»«mi»a«/mi»«mi»b«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§nbsp;«/mo»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#g«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mi»n«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mi»#g«/mi»«/mfenced»«mo»=«/mo»«mi»#k1«/mi»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§nbsp;«/mo»«mi»h«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#h«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mi»n«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mi»#h«/mi»«/mfenced»«mo»=«/mo»«mi»#k2«/mi»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfenced»«mi»#h«/mi»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#g«/mi»«/mfenced»«mo»-«/mo»«mfenced close=¨}¨ open=¨{¨»«mrow»«mfenced»«mi»#g«/mi»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#h«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mi»#h«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfenced»«mi»#h«/mi»«/mfenced»«mo»·«/mo»«mfenced close=¨]¨ open=¨[¨»«mi»#k1«/mi»«/mfenced»«mo»-«/mo»«mfenced close=¨}¨ open=¨{¨»«mrow»«mfenced»«mi»#g«/mi»«/mfenced»«mo»·«/mo»«mfenced close=¨]¨ open=¨[¨»«mi»#k2«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mi»#h«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»#k3«/mi»«mo»-«/mo»«mfenced close=¨}¨ open=¨{¨»«mi»#k4«/mi»«/mfenced»«/mrow»«msup»«mfenced»«mi»#h«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»#k3«/mi»«mi»#k5«/mi»«/mrow»«msup»«mfenced»«mi»#h«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»

Luego,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mi»#prima«/mi»«/math»

]]> 1.0000000 1.0000000 0 0 #prima Bien. Continúa de esa manera.

]]> #sol10 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>FUNCIONES</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PRIMERA</mi><mo> </mo><mi>FUNCION</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>g</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>n</mi></msup><mo>+</mo><mi>c2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c3</mi></mrow><mrow><mi>g</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>n</mi></msup><mo>+</mo><mi>c3</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dg</mi><mo>=</mo><mo>(</mo><mi>n</mi><mo>*</mo><mi>c1</mi><mo>)</mo><msup><mi>x</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c2</mi><mo>*</mo><mo>+</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi style="color:#000000">SEGUNDA</mi><mo style="color:#000000"> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>m</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>h</mi><mo>=</mo><mi>d1</mi><mo>*</mo><msup><mi>x</mi><mi>m</mi></msup><mo>+</mo><mi>d2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d3</mi></mrow><mrow><mi>h</mi><mo>=</mo><mi>d1</mi><mo>*</mo><msup><mi>x</mi><mi>m</mi></msup><mo>+</mo><mi>d3</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>FUNCION</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>g</mi><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mi>g</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mi>h</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k3</mi><mo>=</mo><mi>h</mi><mo>*</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k4</mi><mo>=</mo><mo>(</mo><mi>g</mi><mo>*</mo><mi>k2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k5</mi><mo>=</mo><mo>-</mo><mi>k4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mrow><mi>h</mi><mo>*</mo><mi>k1</mi><mo>-</mo><mi>g</mi><mo>*</mo><mi>k2</mi></mrow><mrow><mo>(</mo><mi>h</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>d3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mo>(</mo><mi>n1</mi><mo>*</mo><mi>t1</mi><mo>+</mo><mi>n2</mi><mo>*</mo><mi>t2</mi><mo>+</mo><mi>n3</mi><mo>*</mo><mi>t3</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>sol</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>sol1</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mo>*</mo><mroot><mi>x</mi><mi>n</mi></mroot></mrow></mfrac><mo>*</mo><mi>h</mi></mrow><mrow><mi>sol1</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>*</mo><mroot><msup><mi>x</mi><mi>e1</mi></msup><mi>n</mi></mroot></mrow></mfrac><mo>*</mo><mi>h</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>*</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>RETRO</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>p1</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mo>*</mo><mroot><mi>x</mi><mi>n</mi></mroot></mrow></mfrac></mrow><mrow><mi>p1</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>*</mo><mroot><msup><mi>x</mi><mi>e1</mi></msup><mi>n</mi></mroot></mrow></mfrac></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mfrac><mn>1</mn><mi>x</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>prima</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>sol1</mi><mo>+</mo><mi>sol2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>g</mi><mo>&apos;</mo><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>h</mi><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>prima</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dg</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>y</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #prima </correctAnswer><correctAnswer type="mathml"> #sol10 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 2.9 Derivada de la div. entre trigonométricas. (23.7) Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»#g«/mi»«mi»#h«/mi»«/mfrac»«/math». Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

Obs.: Ingresa las funciones trigonométricas de la siguiente manera:

- seno(x) se ingresa sen(x)

-coseno(x) se ingresa cos(x)

-tangente(x) se ingresa tan(x)

-cosecante(x) se ingresa cosec(x)

-secante(x) se ingresa sec(x)

-cotangente(x) se ingresa cot(x)

]]> Solución:

Debemos derivar la función f(#x)=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»#g«/mi»«/mrow»«mrow»«mi»#h«/mi»«/mrow»«/mfrac»«/math», que corresponde al cuociente (división) de dos funciones, por lo tanto, debemos aplicar la regla de la derivada de la división de dos funciones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»/«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»§#8658;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»·«/mo»«mfrac»«mi mathvariant=¨bold-italic¨»d«/mi»«mrow»«mi mathvariant=¨bold-italic¨»d«/mi»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi mathvariant=¨bold-italic¨»g«/mi»«mo»(«/mo»«mi mathvariant=¨bold-italic¨»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»-«/mo»«mfenced close=¨}¨ open=¨{¨»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»·«/mo»«mfrac»«mi mathvariant=¨bold-italic¨»d«/mi»«mrow»«mi mathvariant=¨bold-italic¨»d«/mi»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi mathvariant=¨bold-italic¨»h«/mi»«mo»(«/mo»«mi mathvariant=¨bold-italic¨»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»

Para el caso particular de f(#x)=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»#g«/mi»«/mrow»«mrow»«mi»#h«/mi»«/mrow»«/mfrac»«/math», su derivada queda:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»#g«/mi»«mi»#h«/mi»«/mfrac»«mo»§nbsp;«/mo»«mo»/«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfenced»«mi»#h«/mi»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#g«/mi»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mfenced»«mi»#g«/mi»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced close=¨]¨ open=¨[¨»«mi»#h«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mi»#h«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»S«/mi»«mi»a«/mi»«mi»b«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§nbsp;«/mo»«mi»g«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#g«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mi»n«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mfenced close=¨¨ open=¨{¨»«mtable»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mi»#g1«/mi»«/mfenced»«mo»=«/mo»«mi»#dg1«/mi»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mi»#g2«/mi»«/mfenced»«mo»=«/mo»«mi»#dg2«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§nbsp;«/mo»«mi»h«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#h«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mi»n«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mi»#h«/mi»«/mfenced»«mo»=«/mo»«mi»#ddh«/mi»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mfenced»«mi»#h«/mi»«/mfenced»«mo»·«/mo»«mfenced»«mi»#dg«/mi»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mfenced»«mi»#g«/mi»«/mfenced»«mo»·«/mo»«mfenced»«mi»#ddh«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mi»#h«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»#sol5«/mi»«mo»-«/mo»«mfenced»«mi»#sol6«/mi»«/mfenced»«/mrow»«msup»«mfenced»«mi»#h«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#resp«/mi»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

Luego,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨normal¨»d«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»#x«/mi»«mo»)«/mo»«mo»)«/mo»«/mrow»«mrow»«mi mathvariant=¨normal¨»d«/mi»«mi mathvariant=¨normal¨»#x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi mathvariant=¨normal¨»#resp«/mi»«/math»

]]> 1.0000000 1.0000000 0 0 #resp Bien. Continúa de esa manera.]]> sol Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>FUNCIONES</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>tan</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>DERIVADAS</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd1</mi><mo>=</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd2</mi><mo>=</mo><mo>-</mo><mi>d1</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>DERIVADA</mi><mo> </mo><mi>DE</mi><mo> </mo><mi>TANX</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd3</mi><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mi>d3</mi></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>COEFICIENTES</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>t3</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><mrow><mi>t1</mi><mo>≠</mo><mi>t2</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>t1</mi><mo>≠</mo><mi>t3</mi><mo>∧</mo><mo> </mo><mi>t2</mi><mo>≠</mo><mi>t3</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dg1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><mi>t1</mi><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><mi>t2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dg2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><mi>t2</mi><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>c1</mi><mo>*</mo><mi>t1</mi><mo>+</mo><mi>c2</mi><mo>*</mo><mi>t2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dg</mi><mo>=</mo><mi>dg1</mi><mo>+</mo><mi>dg2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>t3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ddh</mi><mo>=</mo><mi>t3</mi><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>g</mi><mfenced><mi>h</mi></mfenced></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><mi>f</mi><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mrow><mi>h</mi><mo>*</mo><mo>(</mo><mi>dg1</mi><mo>+</mo><mi>dg2</mi><mo>)</mo><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced><mi>g</mi></mfenced><mo>*</mo><mfenced><mi>ddh</mi></mfenced></mtd></mtr></mtable></mfenced></mrow><mrow><mo>(</mo><mi>h</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol5</mi><mo>=</mo><mi>h</mi><mo>*</mo><mo>(</mo><mi>dg1</mi><mo>+</mo><mi>dg2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol6</mi><mo>=</mo><mfenced><mi>g</mi></mfenced><mo>*</mo><mfenced><mi>ddh</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mrow><mi>h</mi><mo>*</mo><mi>k1</mi><mo>-</mo><mi>g</mi><mo>*</mo><mi>k2</mi></mrow><mrow><mo>(</mo><mi>h</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>prima</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>(</mo><mi>f1</mi><mo>)</mo></mrow><mi>dx</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>g</mi><mo>&apos;</mo><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>h</mi><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>resp</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>15</mn><mo>*</mo><mi>tan</mi><mfenced><mi>v</mi></mfenced><mo>-</mo><mn>11</mn><mo>*</mo><mi>cos</mi><mfenced><mi>v</mi></mfenced></mrow><mrow><mi>sen</mi><mfenced><mi>v</mi></mfenced></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><mi>tan</mi><mfenced><mi>v</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><mi>cos</mi><mfenced><mi>v</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sen</mi><mfenced><mi>v</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dg1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><mi>tan</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dg2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>*</mo><mi>sen</mi><mfenced><mi>v</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dh</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dh</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tan</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>15</mn><mo>*</mo><mi>tan</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup><mo>*</mo><mi>sen</mi><mfenced><mi>v</mi></mfenced><mo>+</mo><mn>11</mn><mo>*</mo><mi>sen</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup><mo>+</mo><mn>15</mn><mo>*</mo><mi>sen</mi><mfenced><mi>v</mi></mfenced><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>15</mn><mo>*</mo><mfenced><mrow><mi>tan</mi><mfenced><mi>v</mi></mfenced><mo>*</mo><mi>cos</mi><mfenced><mi>v</mi></mfenced></mrow></mfenced><mo>-</mo><mn>11</mn><mo>*</mo><mi>cos</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup></mtd></mtr></mtable></mfenced></mrow><mrow><mi>sen</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>15</mn><mo>*</mo><mi>tan</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup><mo>*</mo><mi>sen</mi><mfenced><mi>v</mi></mfenced><mo>-</mo><mn>15</mn><mo>*</mo><mi>tan</mi><mfenced><mi>v</mi></mfenced><mo>*</mo><mi>cos</mi><mfenced><mi>v</mi></mfenced><mo>+</mo><mn>11</mn><mo>*</mo><mi>cos</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup><mo>+</mo><mn>11</mn><mo>*</mo><mi>sen</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup><mo>+</mo><mn>15</mn><mo>*</mo><mi>sen</mi><mfenced><mi>v</mi></mfenced></mrow><mrow><mi>sen</mi><msup><mfenced><mi>v</mi></mfenced><mn>2</mn></msup></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #resp </correctAnswer><correctAnswer type="mathml"> sol </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 3.1 Derivada de la división entre un polinomio y una trigonométrica. Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math». Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

Obs.: Ingresa las funciones trigonométricas de las siguiente manera:

- seno(x) se ingresa sen(x)

- coseno(x) se ingresa cos(x)

- tangente(x) se ingresa tan(x)

- cosecante(x) se ingresa cosec(x)

- secante(x) se ingresa sec(x)

- cotangente(x) se ingresa cotan(x)

]]> Solución:

La función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math» corresponde a un cuociente de funciones, por lo tanto, aplicaremos la regla de la derivada para el cuociente (división) de funciones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mfrac»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»-«/mo»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/mrow»«msup»«mfenced»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mo»§nbsp;«/mo»«mo»,«/mo»«mo»§nbsp;«/mo»«mo»§#8704;«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#8800;«/mo»«mn»0«/mn»«/math»

En nuestro caso:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr3«/mi»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»A«/mi»«mi»p«/mi»«mi»l«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§nbsp;«/mo»«mi»á«/mi»«mi»l«/mi»«mi»g«/mi»«mi»e«/mi»«mi»b«/mi»«mi»r«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»v«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»v«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»c«/mi»«mi»i«/mi»«mi»ó«/mi»«mi»n«/mi»«mo»§nbsp;«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mi»g«/mi»«mi»o«/mi»«mi»n«/mi»«mi»o«/mi»«mi»m«/mi»«mi»é«/mi»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mo»:«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr4«/mi»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»A«/mi»«mi»p«/mi»«mi»l«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»v«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»t«/mi»«mi»e«/mi»«mi»n«/mi»«mi»c«/mi»«mi»i«/mi»«mi»a«/mi»«mo»:«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr5«/mi»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»A«/mi»«mi»l«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»s«/mi»«mi»a«/mi»«mi»r«/mi»«mi»r«/mi»«mi»o«/mi»«mi»l«/mi»«mi»l«/mi»«mi»a«/mi»«mi»r«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mi»m«/mi»«mi»u«/mi»«mi»l«/mi»«mi»t«/mi»«mi»i«/mi»«mi»p«/mi»«mi»l«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mi»c«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»o«/mi»«mi»r«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»l«/mi»«mo»§nbsp;«/mo»«mi»p«/mi»«mi»r«/mi»«mi»i«/mi»«mi»m«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§nbsp;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»s«/mi»«mi»i«/mi»«mi»s«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»s«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»o«/mi»«mi»b«/mi»«mi»t«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»e«/mi»«mo»:«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr6«/mi»«/mtd»«/mtr»«/mtable»«/math»

Por lo tanto,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr6«/mi»«/math»

]]> 1.0000000 1.0000000 0 0 #resp ¡Muy Bien! Sigue así.]]> #sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ABC</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mi>z</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi>w</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><msub><mi>ABC</mi><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>POL</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>k</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>2</mn></mrow></msup><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>2</mn></mrow></msup><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>(</mo><mo>#</mo><mn>2</mn><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>3</mn></mrow></msup><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>)</mo></mrow><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>(</mo><mn>2</mn><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mi>n</mi></mrow><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mo>(</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mn>1</mn><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mo>(</mo><mn>0</mn><mo>)</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable></apply></apply></mtd></mtr></mtable><mrow><mi>k</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mi>s</mi><mo>+</mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>-</mo><mi>c</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><msup><mi>X</mi><mi>c</mi></msup></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>c</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable><mrow><mi>c</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold4</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold4</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&gt;</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>k</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>pold2</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mrow><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow><mrow><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced></mrow></apply></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>pold2</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mrow><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow><mrow><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced></mrow></apply></mtd></mtr></mtable></apply></mtd></mtr></mtable><mrow><mi>k</mi><mo>=</mo><mi>n</mi></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>pold2</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>pold2</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>2</mn></mrow></mfrac><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><mi>X</mi></mrow></mfenced></math></input></command><command><input><math 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</mo><mo>&verbar;</mo><mo> 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</mo><mo>&verbar;</mo><mo> </mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>cosec</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mi>cotan</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd><mtd><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd><mtd><mi>cosec</mi><mo>(</mo><mi>X</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>sec</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mi>sec</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd><mtd><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>sec</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mi>tan</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd><mtd><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd><mtd><mi>sec</mi><mo>(</mo><mi>X</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>cotan</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mi>cotan</mi><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd><mtd><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> 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</mo><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>#</mo><mn>4</mn></mrow><mrow><mo>(</mo><mo>#</mo><mn>3</mn><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pold1</mi><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold2</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr6</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold4</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ftrig</mi><mo>=</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math 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ced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac></mfenced><mo>*</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mn>1</mn><mo>*</mo><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mn>0</mn></mfenced></mrow><mrow><mi>cos</mi><mfenced><mn>0</mn></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mn>0</mn><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>tan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mfrac><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><msup><mi>cos</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><msup><mi>sen</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mn>1</mn><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><msup><mi>sec</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cosec</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mfrac><mn>1</mn><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mn>1</mn></mfenced><mo>*</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>*</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mn>0</mn><mo>*</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>-</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mfrac><mn>1</mn><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>*</mo><mfrac><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mi>cosec</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>cotan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>5</mn></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>sec</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mfrac><mn>1</mn><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mn>1</mn></mfenced><mo>*</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>*</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mn>0</mn><mo>*</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>*</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>*</mo><mfrac><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mi>sec</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>tan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cotan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mfrac><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>-</mo><msup><mi>sen</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><msup><mi>cos</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><msup><mi>cosec</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow></apply></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dftrig</mi><mo>=</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>exr6</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cot</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cotan</mi><mfenced><mi>x</mi></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #resp </correctAnswer><correctAnswer type="mathml"> #sol2 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 3.1 Derivada de la división entre un polinomio y una trigonométrica. (EVALUACIÓN) Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math». Entonces, #Z

#GRAF

Obs.: Puede ingresar la respuesta exacta (en función de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«/math» ) o la respuesta aproximada considerando 2 decimales de precisión.

]]> Solución:

En nuestro caso:

¿Que significado tiene para la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«/math» que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mi»p«/mi»«mi»r«/mi»«mi»o«/mi»«mi»x«/mi»«mi»i«/mi»«mi»m«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«mi»m«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mi»#x1«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#valorresultado«/mi»«/math»?
En general, ¿Que es lo que representa la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«/math»?

]]> 1.0000000 1.0000000 0 0 #resultado ¡Muy Bien! Sigue así.]]> #sol2 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ABC</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mi>z</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi>w</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><msub><mi>ABC</mi><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><pi/><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>6</mn></mfrac></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>POL</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>k</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>2</mn></mrow></msup><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mrow><mo>#</mo><mn>2</mn></mrow></msup><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>2</mn></mrow></msup><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>(</mo><mo>#</mo><mn>2</mn><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>3</mn></mrow></msup><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>)</mo></mrow><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>(</mo><mn>2</mn><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mi>n</mi></mrow><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mo>(</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mn>1</mn><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mn>1</mn><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mo>(</mo><mn>0</mn><mo>)</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable></apply></apply></mtd></mtr></mtable><mrow><mi>k</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mi>s1</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold4</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> 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open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold4</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&gt;</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>k</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>pold2</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced></mtd></mtr></mtable></apply></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>pold2</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> 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</mo><mo>&verbar;</mo><mo> </mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><msup><mi>cosec</mi><mn>2</mn></msup><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd><mtd><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd><mtd><mi>cotan</mi><mo>(</mo><mi>X</mi><mo>)</mo></mtd><mtd><mi>cotan</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mi>cotan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd><mtd><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><msup><mi>cosec</mi><mn>2</mn></msup><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mfenced><mrow><mi>t1</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mi>s1</mi><mfenced><mi>x</mi></mfenced></mrow><mrow><mi>t1</mi><mfenced><mi>x</mi></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mfrac><mrow><mi>g1</mi><mfenced><mi>x1</mi></mfenced></mrow><mn>2</mn></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mi>g1</mi><mfenced><mi>x1</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow><mi>P</mi><mo>,</mo><mn>20</mn><mo>,</mo><mn>2</mn><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mrow><mi>g1</mi><mfenced><mi>x1</mi></mfenced></mrow></mfenced><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>GRAF</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mtable align="center"><mtr><mtd><mi>g1</mi></mtd></mtr></mtable></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>QR</mi><mo>=</mo><mi>segmento</mi><mfenced><mrow><mi>Q</mi><mo>,</mo><mi>R</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>R</mi><mo>,</mo><mfenced close="}" open="{"><mrow><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>10</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>QR</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>escribir</mi><mfenced><mrow><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>=</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>x1</mi></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr1</mi><mo>=</mo><mfrac><mi>pol</mi><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>3</mn></mrow></mfrac><mfenced><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>X</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr3</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mo> </mo><mo>-</mo><mo> </mo><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>#</mo><mn>4</mn></mrow><mrow><mo>(</mo><mo>#</mo><mn>3</mn><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pold1</mi><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold2</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold3</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr6</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold4</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr7</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pold6</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub><mo>,</mo><mi>pold5</mi><mo>,</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ftrig</mi><mo>=</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><mi>derivar</mi><mfenced><mfrac><mi>s</mi><mi>t</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mfrac><mrow><mi>r1</mi><mfenced><mi>x1</mi></mfenced><mo>*</mo><mi>t1</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>-</mo><mi>s1</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>u1</mi><mfenced><mi>x1</mi></mfenced></mrow><mrow><mi>v1</mi><mo>(</mo><mi>x1</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valorresultado</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mrow><mi>redondear</mi><mfenced><mrow><mi>resultado</mi><mo>*</mo><mn>100</mn></mrow></mfenced><mo>/</mo><mn>100</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>sen</mi><mfenced><mrow><mi>h</mi><mo>+</mo><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mi>h</mi></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mi>h</mi></mfenced><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mi>h</mi></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>-</mo><mn>1</mn></mrow><mi>h</mi></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>-</mo><mn>1</mn></mrow><mi>h</mi></mfrac></mfenced><mfenced><mfrac><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><msup><mi>cos</mi><mn>2</mn></msup><mfenced><mi>h</mi></mfenced><mo>-</mo><mn>1</mn></mrow><mrow><mi>h</mi><mfenced><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><msup><mi>sen</mi><mn>2</mn></msup><mfenced><mi>h</mi></mfenced></mrow><mrow><mi>h</mi><mfenced><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac></mfenced><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac></mfenced><mo>*</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mn>1</mn><mo>*</mo><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mn>0</mn></mfenced></mrow><mrow><mi>cos</mi><mfenced><mn>0</mn></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mn>0</mn><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>cos</mi><mfenced><mrow><mi>h</mi><mo>+</mo><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mi>h</mi></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>sen</mi><mfenced><mi>h</mi></mfenced><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mi>h</mi></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>-</mo><mn>1</mn></mrow><mi>h</mi></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>-</mo><mn>1</mn></mrow><mi>h</mi></mfrac></mfenced><mfenced><mfrac><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><msup><mi>cos</mi><mn>2</mn></msup><mfenced><mi>h</mi></mfenced><mo>-</mo><mn>1</mn></mrow><mrow><mi>h</mi><mfenced><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><msup><mi>sen</mi><mn>2</mn></msup><mfenced><mi>h</mi></mfenced></mrow><mrow><mi>h</mi><mfenced><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac></mfenced><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mfrac><mrow><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mi>h</mi></mfrac></mfenced><mo>*</mo><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mi>h</mi></mfenced></mrow><mrow><mi>cos</mi><mfenced><mi>h</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mn>1</mn><mo>*</mo><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mn>0</mn></mfenced></mrow><mrow><mi>cos</mi><mfenced><mn>0</mn></mfenced><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mfrac><mn>0</mn><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>tan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mfrac><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><msup><mi>cos</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>+</mo><msup><mi>sen</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mn>1</mn><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><msup><mi>sec</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cosec</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mfrac><mn>1</mn><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mn>1</mn></mfenced><mo>*</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>*</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mn>0</mn><mo>*</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>-</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mfrac><mn>1</mn><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>*</mo><mfrac><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mi>cosec</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>cotan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>5</mn></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>sec</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mfrac><mn>1</mn><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mn>1</mn></mfenced><mo>*</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>*</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mn>0</mn><mo>*</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>*</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>*</mo><mfrac><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mi>sec</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>tan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow><mrow><mi>mtrxdemdrtrig</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mi>d</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cotan</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mfrac><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>-</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>cos</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>-</mo><msup><mi>sen</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>-</mo><msup><mi>cos</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><msup><mfenced><mrow><mi>sen</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><msup><mi>cosec</mi><mn>2</mn></msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></mrow></apply></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dftrig</mi><mo>=</mo><msub><mi>TRIG</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inf</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mfenced><mrow><mfenced close="⌋" open="⌊"><mrow><mi>resultado</mi><mo>*</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mn>10</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sup</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mfenced><mrow><mfenced close="⌉" open="⌈"><mrow><mi>resultado</mi><mo>*</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mn>10</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test1</mi><mfenced><mi>x</mi></mfenced><mo>:=</mo><mfenced><mrow><mi>x</mi><mo>&ges;</mo><mi>inf</mi><mo>∧</mo><mi>x</mi><mo>&les;</mo><mi>sup</mi></mrow></mfenced><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test2</mi><mfenced><mi>x</mi></mfenced><mo>:=</mo><mfenced><mrow><mi>x</mi><mo>&lt;</mo><mi>inf</mi><mo>∨</mo><mi>x</mi><mo>&gt;</mo><mi>sup</mi></mrow></mfenced><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>X</mi><mo>=</mo><mi>x1</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>&quot;</mo><mi>es</mi><mo> </mo><mi>igual</mi><mo> </mo><mi>a</mi><mo>:</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>vale</mi><mo>:</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><apply><diff/><bvar><mrow><mo>#</mo><mn>2</mn></mrow></bvar><mrow><mi>f</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></apply><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>X</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>pendiente</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>tangente</mi><mo> </mo><mi>a</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>evaluación</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>Z1</mi><mo>,</mo><mi>Z2</mi><mo>,</mo><mi>Z3</mi><mo>,</mo><mi>Z4</mi><mo>}</mo></math></input></command></group></library></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #resultado </correctAnswer><correctAnswer type="mathml"> #sol2 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test1</param></assertion><assertion name="equivalent_function" correctAnswer="1"><param name="name">test2</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 3.2 Derivada de la división entre un polinomio y una raíz. Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math». Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»

]]>

Solución:

La función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math», corresponde a un cuociente de funciones, por lo tanto, aplicaremos la regla de la derivada para el cuociente (división) de funciones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfenced»«mfrac»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»-«/mo»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»

En nuestro caso, aplicando la regla:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr3«/mi»«/math»

Aplicando la derivada de una potencia y la derivada de una raíz:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«mi»#exr5«/mi»«/math»
Desarrollando las operaciones dentro del primer paréntesis:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr6«/mi»«/math»

Reescribiendo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr7«/mi»«/math» =

Desarrollando el producto de las raices y utilizando las propiedades de potencias obtenemos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr8«/mi»«/math»

Desarrollando el producto de los términos de los primeros dos paréntesis:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr9«/mi»«/math»

Aplicando el cambio de signo de los elementos del paréntesis:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr10«/mi»«/math»

Sumando términos semejantes obtenemos finalmente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr11«/mi»«/math»

Por lo tanto,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr11«/mi»«/math»

Recuerda que no es la única forma de escribir el resultado. Si descompones la raíz del denominador, también la puedes escribir así:

]]> 1.0000000 1.0000000 0 0 #resp ¡Muy Bien! Sigue así.
]]> #sol10 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ABC</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mi>z</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi>w</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><msub><mi>ABC</mi><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>RAIZ</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mroot><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi></mrow></mfenced></mtd><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mroot><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi></mrow></mfenced></mtd><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>3</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>m</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mtd><mtd><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>3</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>m</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mtd><mtd><mroot><mi>X</mi><mi>m</mi></mroot></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>POL</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>k</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>2</mn></mrow></msup><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>2</mn></mrow></msup><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfenced><mrow><mo>#</mo><mn>2</mn><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>3</mn></mrow></msup></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>-</mo><mi>k</mi></mrow></mfenced></mrow><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>(</mo><mn>2</mn><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>*</mo><mi>m</mi></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>+</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mi>n</mi></mrow><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mo>(</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>*</mo><mi>m</mi></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>+</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mn>1</mn><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mo>(</mo><mn>1</mn><mo>)</mo><mo>&quot;</mo><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mo>&quot;</mo><mo>(</mo><mn>0</mn><mo>)</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub><mo>*</mo><mi>m</mi></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub><mo>=</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub><mo>+</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub></mtd></mtr></mtable></apply></apply></mtd></mtr></mtable><mrow><mi>k</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math 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close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold7</mi><mo>=</mo><mi>pold7</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo>,</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced><mo> </mo></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold7</mi><mo>=</mo><mi>pold7</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></apply></mtd></mtr></mtable><mrow><mi>k</mi><mo>=</mo><mi>n</mi></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi><mo>,</mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced><mo> </mo></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>7</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold7</mi><mo>=</mo><mi>pold7</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>8</mn></mrow></msub></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo>,</mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>7</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold7</mi><mo>=</mo><mi>pold7</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>8</mn></mrow></msub></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&apos;</mo><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold11</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>pol</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr1</mi><mo>=</mo><mfrac><mi>pol</mi><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>3</mn></mrow></mfrac><mfenced><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>X</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr3</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>3</mn><mo>*</mo><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mo>#</mo><mn>4</mn></mrow><mrow><mo>(</mo><mo>#</mo><mn>2</mn><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold11</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold2</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow></mfenced><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold3</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr6</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow></mfenced><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold4</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr7</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>(</mo><mo>#</mo><mn>4</mn><mo>)</mo><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mrow><mo>(</mo><mo>#</mo><mn>4</mn><mo>)</mo><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold4</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr8</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn><mo>#</mo><mn>4</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>pold4</mi><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr9</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>pold5</mi><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr10</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mo>#</mo><mn>3</mn><mo>#</mo><mn>1</mn></mrow></mfenced><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pold6</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>pold5</mi><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr11</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>3</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pold7</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><mi>derivar</mi><mfenced><mfrac><mi>s</mi><mi>r</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>≠</mo><mi>resp</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>POL</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><msup><mi>w</mi><mn>3</mn></msup></mtd><mtd><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><msup><mi>w</mi><mn>3</mn></msup><ms>)</ms></mtd><mtd><mfenced><mrow><mn>3</mn><msup><mi>w</mi><mn>2</mn></msup></mrow></mfenced></mtd><mtd><mo>-</mo><mn>12</mn></mtd><mtd><mo>-</mo><mn>48</mn></mtd><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mn>44</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><msup><mi>w</mi><mn>2</mn></msup></mtd><mtd><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><msup><mi>w</mi><mn>2</mn></msup><ms>)</ms></mtd><mtd><ms>(2</ms><mi>w</mi><ms>)</ms></mtd><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mo>-</mo><mn>24</mn></mtd><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>21</mn></mtd></mtr><mtr><mtd><mn>9</mn></mtd><mtd><mi>w</mi></mtd><mtd><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><mi>w</mi><ms>)</ms></mtd><mtd><ms>(1)</ms></mtd><mtd><mn>9</mn></mtd><mtd><mn>36</mn></mtd><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mn>27</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>8</mn></mtd><mtd><ms>1</ms></mtd><mtd><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(1)</ms></mtd><mtd><ms>(0)</ms></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>8</mn></mtd><mtd><mn>8</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>48</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>24</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>36</ms><mi>w</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow><mroot><mi>w</mi><mn>4</mn></mroot></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><mfenced><mfrac><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow><mroot><mi>w</mi><mn>4</mn></mroot></mfrac></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><mfenced><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow></mfenced><mo>*</mo><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow></mfenced><mo>*</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced></mrow><mrow><mo>(</mo><mroot><mi>w</mi><mn>4</mn></mroot><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mo>-</mo><mn>4</mn><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><msup><mi>w</mi><mn>3</mn></msup><ms>)</ms><mo>-</mo><mn>3</mn><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><msup><mi>w</mi><mn>2</mn></msup><ms>)</ms><mo>+</mo><mn>9</mn><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><mi>w</mi><ms>)</ms><mo>-</mo><mn>8</mn><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(1)</ms></mrow></mfenced><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow></mfenced><mfenced><mfrac><mn>1</mn><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot></mrow></mfrac></mfenced></mrow><msup><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>4</mn><mfenced><mrow><mn>3</mn><msup><mi>w</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><ms>3(2</ms><mi>w</mi><ms>)</ms><mo>+</mo><ms>9(1)</ms><mo>-</mo><ms>8(0)</ms></mrow></mfenced><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow></mfenced><mfenced><mfrac><mn>1</mn><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot></mrow></mfrac></mfenced></mrow></mfenced><msup><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>12</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>6</ms><mi>w</mi><mo>+</mo><ms>9</ms></mrow></mfenced><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow></mfenced><mfenced><mfrac><mn>1</mn><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot></mrow></mfrac></mfenced></mrow></mfenced><msup><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>12</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>6</ms><mi>w</mi><mo>+</mo><ms>9</ms></mrow></mfenced><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>(</mo><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot><mo>)</mo><mo>-</mo><mfenced><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow></mfenced></mrow></mfenced><mrow><mo>(</mo><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot><mo>)</mo><msup><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mn>2</mn></msup></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr8</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>12</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>6</ms><mi>w</mi><mo>+</mo><ms>9</ms></mrow></mfenced><mfenced><mrow><mn>4</mn><mi>w</mi></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow></mfenced></mrow></mfenced><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr9</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mo>-</mo><mn>48</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>24</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>36</ms><mi>w</mi><mo>-</mo><mfenced><mrow><mo>-</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>9</ms><mi>w</mi><mo>-</mo><ms>8</ms></mrow></mfenced></mrow></mfenced><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr10</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mo>-</mo><mn>48</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>24</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>36</ms><mi>w</mi><mo>+</mo><mn>4</mn><msup><mi>w</mi><mn>3</mn></msup><mo>+</mo><ms>3</ms><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>9</ms><mi>w</mi><mo>+</mo><ms>8</ms></mrow></mfenced><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>44</mn><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><ms>21</ms><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>27</ms><mi>w</mi><mo>+</mo><ms>8</ms></mrow><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>44</mn><mo>*</mo><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><mn>21</mn><mo>*</mo><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><mn>27</mn><mo>*</mo><mi>w</mi><mo>+</mo><mn>8</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>w</mi><mo>*</mo><mroot><mi>w</mi><mn>4</mn></mroot></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #resp </correctAnswer><correctAnswer type="mathml"> #sol10 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 3.2 Derivada de la división entre un polinomio y una raíz. (EVALUACIÓN) Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math». Entonces, #Z

#GRAF

Obs.: Puede ingresar la respuesta exacta (en formato de fracción) o la respuesta aproximada considerando 2 decimales de precisión.

]]>

Solución:

En nuestro caso, aplicando la regla:

Aplicando la derivada de una potencia y la derivada de una raíz:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«mi»#exr5«/mi»«/math»
Desarrollando las operaciones dentro del primer paréntesis:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr6«/mi»«/math»

Reescribiendo:

Recuerda que no es la única forma de escribir el resultado. Si descompones la raíz del denominador, también la puedes escribir así:

Luego, podemos evaluar en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#X«/mi»«mo»=«/mo»«mi»#x1«/mi»«/math»:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mrow»«mi»#x1«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr12«/mi»«/math»
Al desarrollar la última expresión (labor que dejaremos al estudiantes) se obtiene que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mrow»«mi»#x1«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#resultado«/mi»«mo»§#8776;«/mo»«mi»#valorresultado«/mi»«/math»

Pregunta abierta:
¿podrías calcular la derivada de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math» sin aplicar la regla del cuociente?
¿que significa que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mrow»«mi»#x1«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#resultado«/mi»«mo»§#8776;«/mo»«mi»#valorresultado«/mi»«/math»?

]]> 1.0000000 1.0000000 0 0 #resultado ¡Muy Bien! Sigue así.
]]> #sol10 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ABC</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mi>z</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi>w</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><msub><mi>ABC</mi><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math 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open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>8</mn></mrow></msub></mfenced><mo>,</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pold8</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mo>#</mo><mn>1</mn><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>8</mn></mrow></msub></mfenced><mo>,</mo><msub><mi>POL</mi><mrow><mn>1</mn><mo>,</mo><mn>9</mn></mrow></msub></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&gt;</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>k</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi><mo>,</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold7</mi><mo>=</mo><mi>pold7</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold8</mi><mo>=</mo><mi>pold8</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>9</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo>,</mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced><mo> </mo></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>&lt;</mo><mi>n</mi></mrow><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>pold4</mi><mo>=</mo><mi>pold4</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>5</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold5</mi><mo>=</mo><mi>pold5</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>6</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>7</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold7</mi><mo>=</mo><mi>pold7</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold8</mi><mo>=</mo><mi>pold8</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>8</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>k</mi><mo>,</mo><mn>9</mn></mrow></msub></mtd></mtr></mtable></apply></mtd></mtr></mtable><mrow><mi>k</mi><mo>=</mo><mi>n</mi></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi><mo>,</mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced><mo> </mo></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>7</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold7</mi><mo>=</mo><mi>pold7</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>8</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold8</mi><mo>=</mo><mi>pold8</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>8</mn></mrow></msub></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol</mi><mo>=</mo><mi>pol</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo>,</mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pold3</mi><mo>=</mo><mi>pold3</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfenced><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold6</mi><mo>=</mo><mi>pold6</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>7</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>pold7</mi><mo>=</mo><mi>pold7</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>8</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd><mi>pold8</mi><mo>=</mo><mi>pold8</mi><mo> </mo><mo>&verbar;</mo><mo> </mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mo> </mo><mo>&verbar;</mo><mo> </mo><mfenced close="&verbar;" open="&verbar;"><msub><mi>POL</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>8</mn></mrow></msub></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>&apos;</mo><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold11</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>1</mn></mrow></mfrac><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>pol</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>&quot;</mo><mo>,</mo><mi>pold2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mi>r1</mi><mfenced><mi>x</mi></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mfenced><mrow><mi>r1</mi><mfenced><mi>x</mi></mfenced></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mi>s1</mi><mfenced><mi>x</mi></mfenced></mrow><mrow><mi>r1</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mfrac><mrow><mi>g1</mi><mfenced><mi>x1</mi></mfenced></mrow><mn>2</mn></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mi>g1</mi><mfenced><mi>x1</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow><mi>P</mi><mo>,</mo><mn>20</mn><mo>,</mo><mn>2</mn><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mrow><mi>g1</mi><mfenced><mi>x1</mi></mfenced></mrow></mfenced><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>GRAF</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mtable align="center"><mtr><mtd><mi>g1</mi></mtd></mtr></mtable></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>QR</mi><mo>=</mo><mi>segmento</mi><mfenced><mrow><mi>Q</mi><mo>,</mo><mi>R</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>R</mi><mo>,</mo><mfenced close="}" open="{"><mrow><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>10</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>QR</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>escribir</mi><mfenced><mrow><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>=</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>x1</mi></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr1</mi><mo>=</mo><mfrac><mi>pol</mi><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mo>#</mo><mn>3</mn></mrow></mfrac><mfenced><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>X</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr3</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>3</mn><mo>*</mo><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mo>#</mo><mn>4</mn></mrow><mrow><mo>(</mo><mo>#</mo><mn>2</mn><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold11</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold2</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow></mfenced><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold3</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr6</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>4</mn></mrow></mfenced></mrow></mfenced><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold4</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr7</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>(</mo><mo>#</mo><mn>4</mn><mo>)</mo><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mrow><mo>(</mo><mo>#</mo><mn>4</mn><mo>)</mo><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>pold4</mi><mo>,</mo><msub><mi>RAIZ</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr8</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mo>#</mo><mn>2</mn><mo>#</mo><mn>4</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>pold4</mi><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr9</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pol</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>pold5</mi><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr10</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mfenced><mrow><mo>#</mo><mn>3</mn><mo>#</mo><mn>1</mn></mrow></mfenced><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pold6</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>pold5</mi><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr11</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>3</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pold7</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>X</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr12</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn><mroot><mrow><mo>#</mo><msup><mn>4</mn><mrow><mo>#</mo><mn>5</mn></mrow></msup></mrow><mrow><mo>#</mo><mn>3</mn></mrow></mroot></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>pold8</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><mi>derivar</mi><mfenced><mfrac><mi>s</mi><mi>r</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mfrac><mrow><mi>r2</mi><mfenced><mi>x1</mi></mfenced><mo>*</mo><mi>r1</mi><mfenced><mi>x1</mi></mfenced><mo>-</mo><mi>s1</mi><mfenced><mi>x1</mi></mfenced><mo>*</mo><mi>u1</mi><mfenced><mi>x1</mi></mfenced></mrow><mrow><mi>v1</mi><mfenced><mi>x1</mi></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valorresultado</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mrow><mi>redondear</mi><mfenced><mrow><mi>resultado</mi><mo>*</mo><mn>100</mn></mrow></mfenced><mo>/</mo><mn>100</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inf</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mfenced><mrow><mfenced close="⌋" open="⌊"><mrow><mi>resultado</mi><mo>*</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mn>10</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sup</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mfenced><mrow><mfenced close="⌉" open="⌈"><mrow><mi>resultado</mi><mo>*</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mn>10</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test1</mi><mfenced><mi>x</mi></mfenced><mo>:=</mo><mfenced><mrow><mi>x</mi><mo>&ges;</mo><mi>inf</mi><mo>∧</mo><mi>x</mi><mo>&les;</mo><mi>sup</mi></mrow></mfenced><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test2</mi><mfenced><mi>x</mi></mfenced><mo>:=</mo><mfenced><mrow><mi>x</mi><mo>&lt;</mo><mi>inf</mi><mo>∨</mo><mi>x</mi><mo>&gt;</mo><mi>sup</mi></mrow></mfenced><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>X</mi><mo>=</mo><mi>x1</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>&quot;</mo><mi>es</mi><mo> </mo><mi>igual</mi><mo> </mo><mi>a</mi><mo>:</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>vale</mi><mo>:</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><apply><diff/><bvar><mrow><mo>#</mo><mn>2</mn></mrow></bvar><mrow><mi>f</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></apply><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>X</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>pendiente</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>tangente</mi><mo> </mo><mi>a</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>evaluación</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>Z1</mi><mo>,</mo><mi>Z2</mi><mo>,</mo><mi>Z3</mi><mo>,</mo><mi>Z4</mi><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>POL</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><msup><mi>w</mi><mn>2</mn></msup></mtd><mtd><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><msup><mi>w</mi><mn>2</mn></msup><ms>)</ms></mtd><mtd><ms>(2</ms><mi>w</mi><ms>)</ms></mtd><mtd><mo>-</mo><mn>10</mn></mtd><mtd><mo>-</mo><mn>40</mn></mtd><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>35</mn></mtd><mtd><msup><mfenced><mfrac><mn>1</mn><mn>16</mn></mfrac></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mi>w</mi></mtd><mtd><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><mi>w</mi><ms>)</ms></mtd><mtd><ms>(1)</ms></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mo>-</mo><mn>20</mn></mtd><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>15</mn></mtd><mtd><ms>(</ms><mfrac><mn>1</mn><mn>16</mn></mfrac><ms>)</ms></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><ms>1</ms></mtd><mtd><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(1)</ms></mtd><mtd><ms>(0)</ms></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>5</mn></mtd><mtd><ms>(1)</ms></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pold5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>40</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>20</ms><mi>w</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow><mroot><mi>w</mi><mn>4</mn></mroot></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><mfenced><mfrac><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow><mroot><mi>w</mi><mn>4</mn></mroot></mfrac></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><mfenced><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced><mo>*</mo><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced><mo>*</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced></mrow><mrow><mo>(</mo><mroot><mi>w</mi><mn>4</mn></mroot><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mo>-</mo><mn>5</mn><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><msup><mi>w</mi><mn>2</mn></msup><ms>)</ms><mo>-</mo><mn>5</mn><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(</ms><mi>w</mi><ms>)</ms><mo>-</mo><mn>5</mn><mfrac><mi>d</mi><mrow><mi>d</mi><mi>w</mi></mrow></mfrac><ms>(1)</ms></mrow></mfenced><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced><mfenced><mfrac><mn>1</mn><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot></mrow></mfrac></mfenced></mrow><msup><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>5</mn><ms>(2</ms><mi>w</mi><ms>)</ms><mo>-</mo><ms>5(1)</ms><mo>-</mo><ms>5(0)</ms></mrow></mfenced><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced><mfenced><mfrac><mn>1</mn><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot></mrow></mfrac></mfenced></mrow></mfenced><msup><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>10</mn><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced><mfenced><mfrac><mn>1</mn><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot></mrow></mfrac></mfenced></mrow></mfenced><msup><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>10</mn><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mo>(</mo><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot><mo>)</mo><mo>-</mo><mfenced><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced></mrow></mfenced><mrow><mo>(</mo><mn>4</mn><mroot><msup><mi>w</mi><mn>3</mn></msup><mn>4</mn></mroot><mo>)</mo><msup><mfenced><mroot><mi>w</mi><mn>4</mn></mroot></mfenced><mn>2</mn></msup></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr8</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>10</mn><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced><mfenced><mrow><mn>4</mn><mi>w</mi></mrow></mfenced><mo>-</mo><mfenced><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced></mrow></mfenced><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr9</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mo>-</mo><mn>40</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>20</ms><mi>w</mi><mo>-</mo><mfenced><mrow><mo>-</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>5</ms><mi>w</mi><mo>-</mo><ms>5</ms></mrow></mfenced></mrow></mfenced><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr10</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mo>-</mo><mn>40</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>20</ms><mi>w</mi><mo>+</mo><mn>5</mn><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>5</ms><mi>w</mi><mo>+</mo><ms>5</ms></mrow></mfenced><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>35</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><ms>15</ms><mi>w</mi><mo>+</mo><ms>5</ms></mrow><mrow><mn>4</mn><mroot><msup><mi>w</mi><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exr12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>35</mn><msup><mfenced><mfrac><mn>1</mn><mn>16</mn></mfrac></mfenced><mn>2</mn></msup><mo>-</mo><ms>15(</ms><mfrac><mn>1</mn><mn>16</mn></mfrac><ms>)</ms><mo>+</mo><ms>5</ms></mrow><mrow><mn>4</mn><mroot><msup><mfrac><mn>1</mn><mn>16</mn></mfrac><mn>5</mn></msup><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>35</mn><mo>*</mo><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><mn>15</mn><mo>*</mo><mi>w</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>w</mi><mo>*</mo><mroot><mi>w</mi><mn>4</mn></mroot></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1005</mn><mn>32</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valorresultado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>31.41</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #resultado </correctAnswer><correctAnswer type="mathml"> #sol10 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test1</param></assertion><assertion name="equivalent_function" correctAnswer="1"><param name="name">test2</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> RA5 3.3 Derivada de la división entre un polinomio y un logaritmo. Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«/mrow»«mi»#pol1«/mi»«/mfrac»«/math». Entonces, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»
]]> Solución:

La función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«/mrow»«mi»#pol1«/mi»«/mfrac»«/math», corresponde a un cuociente de funciones, por lo tanto, aplicaremos la regla de la derivada del cuociente (división) de funciones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mfrac»«mrow»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«mrow»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«mo»·«/mo»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»-«/mo»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»

Aplicando la regla a nuestra función:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#pol1«/mi»«mo»)«/mo»«mo»-«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfrac»«mrow»«mi»d«/mi»«mfenced»«mi»#pol1«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«/mrow»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»

Aplicando la derivada de del logaritmo natural y la derivada de una potencia:

Desarrollando:

Por lo tanto:

]]> 1.0000000 1.0000000 0 0 #resp ¡Excelente!]]> #sol10 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

#GRAF

Obs.: Puede ingresar la respuesta exacta o la respuesta aproximada considerando 6 decimales de precisión.

]]> Solución:

Aplicando la regla a nuestra función:

Aplicando la derivada de del logaritmo natural y la derivada de una potencia:

Desarrollando:

Por lo tanto:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mrow»«mi»#pol1«/mi»«mo»-«/mo»«mi»#X«/mi»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfenced»«mi»#pol3«/mi»«/mfenced»«/mrow»«mrow»«mi»#X«/mi»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»
Luego, podemos evaluar en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#X«/mi»«mo»=«/mo»«mi»#x1«/mi»«/math»:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mrow»«mi»#x1«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»#pol4«/mi»«mo»-«/mo»«mi»#x1«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mrow»«mi»#x1«/mi»«/mrow»«/mfenced»«mo»§nbsp;«/mo»«mfenced»«mrow»«mi»#pol5«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»#x1«/mi»«mo»§nbsp;«/mo»«msup»«mfenced»«mrow»«mi»#pol4«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/math»

Al desarrollar la última expresión (labor que dejaremos al estudiante) se obtiene que:

]]> 1.0000000 1.0000000 0 0 #resultado ¡Excelente!]]> #sol10 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>w</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AUX</mi><mo>=</mo><mi>X</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>ln</mi><mfenced><mi>X</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>ln</mi><mfenced><mi>x</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>po</mi><mo>=</mo><mi>A</mi><mo>*</mo><msup><mi>X</mi><mn>2</mn></msup><mo>+</mo><mi>B</mi><mo>*</mo><mi>X</mi><mo>+</mo><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>A</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>B</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>l1</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>p1</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dq1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mi>q1</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mfrac><mrow><mi>q1</mi><mfenced><mi>x1</mi></mfenced></mrow><mn>2</mn></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>,</mo><mi>q1</mi><mfenced><mi>x1</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow><mi>P</mi><mo>,</mo><mn>20</mn><mo>,</mo><mn>2</mn><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mrow><mi>q1</mi><mfenced><mi>x1</mi></mfenced></mrow></mfenced><mo>+</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>GRAF</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mtable align="center"><mtr><mtd><mi>q1</mi></mtd></mtr></mtable></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>QR</mi><mo>=</mo><mi>segmento</mi><mfenced><mrow><mi>Q</mi><mo>,</mo><mi>R</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>R</mi><mo>,</mo><mfenced close="}" open="{"><mrow><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>10</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>QR</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>escribir</mi><mfenced><mrow><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>=</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>X</mi><mo>,</mo><mi>x1</mi></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mi>x1</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><mi>derivar</mi><mfenced><mfrac><mi>lo</mi><mi>po</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>A</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>#</mo><msup><mn>2</mn><mn>2</mn></msup><mo>&quot;</mo><mo>,</mo><mi>A</mi><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mfenced><mrow><mn>2</mn><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>A</mi><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol3</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>*</mo><mi>A</mi><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>&quot;</mo><mo>,</mo><mi>A</mi><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>*</mo><mi>A</mi><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mo>#</mo><mn>1</mn><mo>#</mo><msup><mn>2</mn><mn>2</mn></msup><mo>&quot;</mo><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mo>#</mo><mn>1</mn><mfenced><mrow><mn>2</mn><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol3</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mo>#</mo><mn>1</mn><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mo>#</mo><mn>1</mn><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>&quot;</mo><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mo>#</mo><mn>1</mn><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>B</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mfenced><mn>1</mn></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol2</mi><mo>,</mo><mi>B</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol3</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol3</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol4</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol5</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced 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open="&verbar;"><mi>B</mi></mfenced><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol5</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>B</mi></mfenced><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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</mo><mi>a</mi><mo>:</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>vale</mi><mo>:</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><apply><diff/><bvar><mrow><mo>#</mo><mn>2</mn></mrow></bvar><mrow><mi>f</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></apply><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>X</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>pendiente</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>tangente</mi><mo> </mo><mi>a</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>evaluación</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>Z1</mi><mo>,</mo><mi>Z2</mi><mo>,</mo><mi>Z3</mi><mo>,</mo><mi>Z4</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>AUX</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mi>w</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mfenced><mrow><mn>2</mn><mi>w</mi></mrow></mfenced><mo>-</mo><mn>5</mn><mfenced><mn>1</mn></mfenced><mo>-</mo><mn>5</mn><mfenced><mn>0</mn></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mi>w</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msup><mfenced><mn>5</mn></mfenced><mn>2</mn></msup><mo>-</mo><mn>5</mn><mfenced><mn>5</mn></mfenced><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mfenced><mn>5</mn></mfenced><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0.0086388</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mo>-</mo><mn>8</mn><mo>*</mo><mi>w</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mi>ln</mi><mfenced><mi>w</mi></mfenced></mrow><mrow><mn>16</mn><mo>*</mo><msup><mi>w</mi><mn>4</mn></msup><mo>-</mo><mn>40</mn><mo>*</mo><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><mn>15</mn><mo>*</mo><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><mi>w</mi><mo>+</mo><mn>25</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mo>*</mo><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>w</mi></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #resultado </correctAnswer><correctAnswer type="mathml"> #sol10 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test1</param></assertion><assertion name="equivalent_function" correctAnswer="1"><param name="name">test2</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question>

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«/math»	/ Ocupando la identidad «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math» tenemos:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mfrac»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«/math»	/ Ocupando (2),tenemos:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»·«/mo»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»-«/mo»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mo»=«/mo»«/math»	/ Ocupando la propiedad (3) enunciada al inicio de la resolución, tenemos:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»-«/mo»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mo»-«/mo»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mo»=«/mo»«/math»	/ Desarrollando los productos del numerador:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»sen«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«/math»	/ Separando en suma de dos fracciones:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«menclose notation=¨updiagonalstrike¨»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/menclose»«menclose notation=¨updiagonalstrike¨»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/menclose»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»s«/mi»«mi»e«/mi»«msup»«mi»n«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«/math»	/ Ocupando «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi mathvariant=¨normal¨»cos«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math», se obtiene finalmente:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»tan«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/math»

Por lo tanto,	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»tan«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/math» (4)