CÁLCULO/4. DERIVADAS/1 Algebra de derivadas 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>