Cálculo diferencial/DERIVADAS /INTERPRETACIÓN GEOMÉTRICA Y FÍSICA DE LA DERIVADA INT1 CD DERIVADAS recta tangente INT1

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, #Z

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

]]> 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:

«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»«mfrac»«mrow»«mfenced»«mfrac»«mn»1«/mn»«mi»#X«/mi»«/mfrac»«/mfenced»«mo»(«/mo»«mi»#pol1«/mi»«mo»)«/mo»«mo»-«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfenced»«mrow»«mi»#pol2«/mi»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/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»«mfrac»«mn»1«/mn»«mi»#X«/mi»«/mfrac»«/mfenced»«mo»(«/mo»«mi»#pol1«/mi»«mo»)«/mo»«mo»-«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfenced»«mi»#pol3«/mi»«/mfenced»«/mrow»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»

Desarrollando:

«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»«mfrac»«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»«mi»#X«/mi»«/mfrac»«msup»«mfenced»«mi»#pol1«/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»§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»

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><![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>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 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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="|" open="|"><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>"</mo><mo>#</mo><mn>1</mn><mo>=</mo><mo>#</mo><mn>2</mn><mo>"</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 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close="|" open="|"><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>"</mo><mo>-</mo><mo>#</mo><mn>1</mn><mfenced><mrow><mn>2</mn><mo>#</mo><mn>2</mn></mrow></mfenced><mo>"</mo><mo>,</mo><mfenced close="|" open="|"><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>"</mo><mo>-</mo><mo>#</mo><mn>1</mn><mo>#</mo><mn>2</mn><mo>"</mo><mo>,</mo><mn>2</mn><mo>*</mo><mfenced close="|" open="|"><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>"</mo><mo>-</mo><mo>#</mo><mn>1</mn><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>"</mo><mo>,</mo><mfenced close="|" open="|"><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>"</mo><mo>-</mo><mo>#</mo><mn>1</mn><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>"</mo><mo>,</mo><mn>2</mn><mo>*</mo><mfenced close="|" open="|"><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>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>"</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>"</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mfenced><mn>1</mn></mfenced><mo>"</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>"</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>"</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>"</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mo>"</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>"</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>"</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>"</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>"</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced 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open="|"><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>"</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>"</mo><mo>,</mo><mi>pol5</mi><mo>,</mo><mfenced close="|" open="|"><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 definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>C</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>"</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mi>C</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mfenced><mn>0</mn></mfenced><mo>"</mo><mo>,</mo><mi>pol2</mi><mo>,</mo><mi>C</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>"</mo><mo>,</mo><mi>pol4</mi><mo>,</mo><mi>C</mi></mrow></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>"</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced close="|" open="|"><mi>C</mi></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mfenced><mn>0</mn></mfenced><mo>"</mo><mo>,</mo><mi>pol2</mi><mo>,</mo><mfenced close="|" open="|"><mi>C</mi></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>"</mo><mo>,</mo><mi>pol4</mi><mo>,</mo><mfenced close="|" open="|"><mi>C</mi></mfenced></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mi>dq1</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math 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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"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>u</mi><mi>l</mi><mi>t</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi>o</mi></math>]]></correctAnswer><correctAnswer id="1">#sol10</correctAnswer></correctAnswers><assertions><assertion name="equivalent_function" correctAnswer="1"><param name="name">test2</param></assertion><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test1</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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>