Skip to main content
Editing a short answer - math & science question by WIRIS
You have permission to :
Edit this question
General
Category
Default for System (16649)
Test-Lidia
Question name
Question text
<p align="justify"><font size="4" face="times new roman,times,serif"><em>Sea la función <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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»#a«/mi»«mo»=«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>.</em></font></p> <p align="justify"><font size="4" face="times new roman,times,serif"><em>Entonces, #X</em></font></p> <p align="justify"><font size="4" face="times new roman,times,serif"><em></em></font></p> <p align="justify"><font size="4" face="times new roman,times,serif"><em>#gr<span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font size="4" face="times new roman,times,serif"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font color="#990000" size="4" face="times new roman,times,serif"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Obs.:</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font color="#990000" size="4" face="times new roman,times,serif"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">1. La función seno de x se ingresa: sen(x)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font color="#990000" size="4" face="times new roman,times,serif"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">2. La función coseno de x se ingresa: cos(x)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font color="#990000" size="4" face="times new roman,times,serif"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">3. La función tangente de x se ingresa: tan(x)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font color="#990000" size="4" face="times new roman,times,serif"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">4. Puede ingresar la respuesta exacta o aproximada, considerando 2 decimales de precisión.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font size="4" face="times new roman,times,serif"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p>
Default mark
General feedback
<p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i><em>Solución:</em></i></font></p> <p style="text-align: left; font-family: times new roman,times,serif"><font size="4"><i><em>Primero debemos obtener la derivada de <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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»#a«/mi»«mo»=«/mo»«mi»#n1«/mi»«mi»#t1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#t2«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em><em> .</em></i></font></p> <p style="text-align: left; font-family: times new roman,times,serif"><font size="4"><i><em>Ocuparemos las siguientes propiedades:</em></i></font></p> <p style="text-align: left; font-family: times new roman,times,serif"><font size="4"><i><em> <table style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; float: none; border-right-style: none; vertical-align: middle" border="1" rules="none" cellspacing="10" cellpadding="10" width="100%" frame="void"><tbody> <tr> <td style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="33%" colspan="2" align="center"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="10%">(1)<br /> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="33%" colspan="2" align="center"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em> </td> <td style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="10%">(2)<br /> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="45%" align="center"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="45%" align="center"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="10%">(3)<br /> </td> </tr></tbody> </table></em></i></font><font size="4"><i><em></em></i></font></p> <p style="text-align: left; font-family: times new roman,times,serif"><font size="4"><i><em><b>Cálculo de la derivada de la Tangente.</b><br />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.</em></i></font></p> <p style="text-align: left; font-family: times new roman,times,serif"><font size="4"><i><em> <table style="background-image: none; border-bottom-style: none; text-align: center; border-left-style: none; border-top-style: none; float: none; border-right-style: none; vertical-align: middle" border="0" rules="none" width="100%" frame="void"><tbody> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: bottom" valign="top" width="50%"> <blockquote>/ Ocupando la identidad <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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 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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> tenemos: </blockquote> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%"> <blockquote>/ Ocupando (2),tenemos:<br /></blockquote> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%"> <blockquote>/ Ocupando la propiedad (3) enunciada al inicio de la resolución, tenemos:<br /></blockquote> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%"> <blockquote>/ Desarrollando los productos del numerador:<br /></blockquote> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%"> <blockquote>/ Separando en suma de dos fracciones:<br /></blockquote> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%"> <blockquote>/ Ocupando <em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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 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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em>, se obtiene finalmente:<br /></blockquote> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»tan«/mi»«mn»2«/mn»«/msup»«mfenced»«mrow»«mi»#w«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%"><br /> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"><br /> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%"><br /> </td> </tr> <tr> <td style="background-image: none; border-bottom-style: none; text-align: right; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%" align="right"> <blockquote>Por lo tanto,<br /></blockquote> </td> <td style="background-image: none; border-bottom-style: none; text-align: left; border-left-style: none; border-top-style: none; border-right-style: none; vertical-align: middle" valign="top" width="50%"> <blockquote><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> (4)<br /></blockquote> </td> </tr></tbody> </table></em></i></font></p><font size="4"><i><em><font face="times new roman,times,serif"><b>Cálculo de la derivada de la suma de funciones trigonométricas.</b><br />Abordaremos ahora el problema de la derivada de la suma de las funciones trigonométricas. <br />Ocupando la propiedad (1) obtenemos:</font><br /></em></i></font> <p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></i></font></p> <p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i>Ocupando las propiedades (3) y (4) obtenemos:</i></font></p> <p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span></span></span></span></span></span></span></span></i></font></p> <p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><font size="4"><i><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></i></font><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></i></font></p> <p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span></span></span></span></span></span></span></span>Por último, reduciendo términos nos queda:<br /></i></font></p> <p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«mo»=«/mo»«mi»#sol«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></i></font></p> <p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i>Por lo tanto:</i></font></p> <p style="font-family: times new roman,times,serif" align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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¨»«mfrac»«mrow»«mi»d«/mi»«mi»#a«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#sol«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="font-family: times new roman,times,serif" align="justify"><font size="4"><i>Luego, evaluando <span class="nolink"><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»#w«/mi»«mo»=«/mo»«mi»#x1«/mi»«/math»</span></span></span></span></span></span></span></span> en <span class="nolink"><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¨»«mfrac»«mrow»«mi»d«/mi»«mi»#a«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»#w«/mi»«/mrow»«/mfrac»«/math»</span></span></span> obtenemos </span></span></span></span></span></i></font><font size="4"><i><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»#sol2«/mi»«mo»§#8776;«/mo»«mi»#sol3«/mi»«/math»</span></span></span>.</span></span></i></font></p> <p><font size="4"><i><span class="nolink"></span></i></font></p> <p><font size="4"><i><span class="nolink"><font face="Times New Roman">Por lo tanto #X <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#sol2«/mi»«mo»§#8776;«/mo»«mi»#sol3«/mi»«/math»</span></span></span></span></font></span></i></font> </p> <p></p> <p></p> <p style="font-family: times new roman,times,serif" align="justify"><strong><em><font size="4">Pregunta abierta:</font></em></strong></p> <p style="font-family: times new roman,times,serif" align="justify"><strong></strong><em><font size="4">¿Qué significa que #X<span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8776;«/mo»«mi»#sol3«/mi»«mo»?«/mo»«/math»</span></span></font></em><br /></p>
No, case is unimportant
Yes, case must match
Correct answers
You must provide at least one possible answer. The first matching answer will be used to determine the score and feedback. Click the icon next to the answer field to edit the mathematical properties of the answer and the question.
Answer 1
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
<div style="text-align: justify; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif">¡Excelente!</span></font></div>
Answer 2
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
<div style="text-align: justify"><span style="font-variant: normal; font-style: normal; white-space: pre-wrap; color: rgb(0,0,0); font-size: 15px; vertical-align: baseline; font-weight: normal; text-decoration: none"><span style="font-style: italic"><font size="4" face="times new roman,times,serif">Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</font></span></span></div>
Answer 3
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
<div style="text-align: justify; font-style: italic"><font size="4"><span style="font-family: times new roman,times,serif">¡Excelente!</span></font></div>
Answer 4
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
<div style="text-align: justify"><span style="font-variant: normal; font-style: normal; white-space: pre-wrap; color: rgb(0,0,0); font-size: 15px; vertical-align: baseline; font-weight: normal; text-decoration: none"><span style="font-style: italic"><font size="4" face="times new roman,times,serif">Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</font></span></span></div>
Answer 5
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
Settings for multiple tries
Penalty for each incorrect try
100%
50%
33.33333%
25%
20%
10%
0%
Hint 1
Hint text
Hint 2
Hint text
Created / last saved
Created
by
Admin User
on
Wednesday, 15 February 2017, 3:41 PM
Last saved
by
Admin User
on
Wednesday, 15 February 2017, 3:41 PM
There are required fields in this form marked
.