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<div style="text-align: justify; font-style: italic">Si <font size="4"><span style="font-family: times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«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»</span></span></span></span></span>. Entonces, <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«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»</span></span></span></span></span></span></font><br /> <div style="text-align: center"><font size="4"><span style="font-family: times new roman,times,serif"></span></font></div></div>
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<div style="text-align: justify; font-style: italic"> <div style="text-align: center"> <div style="text-align: left"> <div style="text-align: justify; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif">Solución:</span></font></div> <div style="text-align: justify; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif"></span></font><br /></div> <div style="text-align: justify; font-style: italic" align="justify"><font size="4" face="times new roman,times,serif">La función <span class="nolink"><span class="nolink"><span class="nolink">«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»</span></span></span>, corresponde a un cuociente de funciones, por lo tanto, aplicaremos la regla de la derivada para el cuociente (división) de funciones:</font></div> <div style="text-align: justify; font-style: italic" align="justify"><font size="4" face="Times New Roman"></font></div> <div style="text-align: justify; font-style: italic" align="justify"><font size="4" face="Times New Roman"></font></div> <div style="text-align: justify; font-style: italic" align="justify"><font size="4" face="Times New Roman"></font></div> <div style="text-align: justify; font-style: italic"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«moȤnbsp;«/mo»«moȤnbsp;«/mo»«moȤnbsp;«/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»</span></span></span></span></span></div> <div style="text-align: justify; font-style: italic" align="justify"><span class="nolink"><span class="nolink"><font size="4" face="times new roman,times,serif">En nuestro caso, aplicando la regla:</font></span></span></div><span class="nolink"><span class="nolink"></span></span> <div style="text-align: justify; font-style: italic"><br /><font size="4"><span style="font-family: times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«/math»</span></span></span><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«/math»</span></span></span> </span></span><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr3«/mi»«/math»</span></span></span></span></span></span></font></div><span style="font-family: times new roman,times,serif"><span class="nolink"><span class="nolink"></span></span> <div style="text-align: justify; font-style: italic"><br /></div><font size="4" face="Times New Roman"></font> <div style="text-align: justify; font-style: italic"><font size="4">Aplicando la derivada de una potencia y la derivada de una raÃz:</font></div> <div style="text-align: justify; font-style: italic"><font size="4"></font><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«mi»#exr5«/mi»«/math»</span></span></span></span></span> <br /><font size="4"><span style="font-family: times new roman,times,serif"></span></font><font size="4"><span style="font-family: times new roman,times,serif">Desarrollando las operaciones dentro del primer paréntesis:</span></font></div><font size="4"><span style="font-family: times new roman,times,serif"></span></font> <div style="text-align: justify; font-style: italic"><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»</span></span></span><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr6«/mi»«/math»</span></span></span></span></span> </div> <div style="text-align: justify; font-style: italic"><br /><font size="4"><span style="font-family: times new roman,times,serif">Reescribiendo:</span></font></div> <div style="text-align: justify; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif"></span></font><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»</span></span></span></span></span><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr7«/mi»«/math»</span></span></span></span></span> =<br /><br /><font size="4"><span style="font-family: times new roman,times,serif">Desarrollando el producto de las raices y utilizando las propiedades de potencias obtenemos:</span></font><br /><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»</span></span></span></span></span><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr8«/mi»«/math»</span></span></span></span></span> <br /><br /><font size="4"><span style="font-family: times new roman,times,serif">Desarrollando el producto de los términos de los primeros dos paréntesis:</span></font><br /><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»</span></span></span></span></span><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr9«/mi»«/math»</span></span></span></span></span> <br /><br /><font size="4"><span style="font-family: times new roman,times,serif">Aplicando el cambio de signo de los elementos del paréntesis:</span></font><br /><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»</span></span></span></span></span><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr10«/mi»«/math»</span></span></span></span></span> <br /><br /><font size="4"><span style="font-family: times new roman,times,serif">Sumando términos semejantes obtenemos finalmente:</span></font><br /><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr2«/mi»«mo»=«/mo»«/math»</span></span></span></span></span><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#exr11«/mi»«/math»</span></span></span></span></span><br /><br /><font size="4"><span style="font-family: times new roman,times,serif">Por lo tanto, <br /></span></font> <div style="text-align: center; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«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»</span></span></span></span></span></span></font><br /></div> <div style="text-align: justify; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif">Recuerda que no es la única forma de escribir el resultado. Si descompones la raÃz del denominador, también la puedes escribir asÃ:</span></font></div> <div style="text-align: justify; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif"></span></font><br /></div> <div style="text-align: center; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«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»#resp«/mi»«/math»</span></span></span></span></span><br /></span></font> <div style="text-align: left"><font size="4"><span style="font-family: times new roman,times,serif"><span style="font-weight: bold"> <table border="1" width="100%"><tbody> <tr> <td valign="top" width="100%"><font size="4"><span style="font-family: times new roman,times,serif"><span style="font-weight: bold">Pregunta abierta:</span><br style="font-weight: bold" />¿podrÃas calcular la derivada de </span></font><font size="4"><span style="font-family: times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«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»</span></span></span></span></span> sin aplicar la regla del cuociente?<br /></span></font> </td> </tr></tbody> </table></span></span></font><br /></div></div></div></span></div></div><font size="4"><span style="font-family: times new roman,times,serif"></span></font></div>
No, case is unimportant
Yes, case must match
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Answer 1
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<div style="text-align: justify; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif">¡Muy Bien! Sigue asÃ.<br /></span></font></div>
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<font size="4" face="times new roman,times,serif"><em>Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</em></font>
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11.11111%
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