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<p><font style="font-style: italic"><span style="font-family: times new roman,times,serif"></span></font><em><font size="4" face="Times New Roman">Si </font></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">«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»</span><font size="4" face="times new roman,times,serif"><em>. E</em></font></span></span></span></span></span><font size="4" face="times new roman,times,serif"><em>ntonces,</em></font> <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»«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»</span></span></span></span></span></span></span></span></span></p> <p><span class="nolink"><span class="nolink"></span></span></p> <p><span class="nolink"><span class="nolink"><font color="#990000" size="4" face="times new roman,times,serif"><em>Obs.: Ingresa las funciones trigonométricas de la siguiente manera:</em></font></span></span></p> <p><span class="nolink"><span class="nolink"><font color="#990000" size="4" face="times new roman,times,serif"><em>- seno(x) se ingresa sen(x)</em></font></span></span></p> <p><span class="nolink"><span class="nolink"><font color="#990000" size="4" face="times new roman,times,serif"><em>-coseno(x) se ingresa cos(x)</em></font></span></span></p> <p><span class="nolink"><span class="nolink"><font color="#990000" size="4" face="times new roman,times,serif"><em>-tangente(x) se ingresa tan(x)</em></font></span></span></p> <p><span class="nolink"><span class="nolink"><font color="#990000" size="4" face="times new roman,times,serif"><em>-cosecante(x) se ingresa cosec(x)</em></font></span></span></p> <p><span class="nolink"><span class="nolink"><font color="#990000" size="4" face="times new roman,times,serif"><em>-secante(x) se ingresa sec(x)</em></font></span></span></p> <p><span class="nolink"><span class="nolink"><font color="#990000" size="4" face="times new roman,times,serif"><em>-cotangente(x) se ingresa cot(x)</em></font></span></span></p> <p><br /></p>
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<p align="justify"><font style="font-style: italic" size="4"><span style="font-family: times new roman,times,serif">Solución:</span><br style="font-family: times new roman,times,serif" /><br style="font-family: times new roman,times,serif" /><span style="font-family: times new roman,times,serif">Debemos derivar la función f(#x)=<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»#g«/mi»«/mrow»«mrow»«mi»#h«/mi»«/mrow»«/mfrac»«/math»</span></span></span></span></span></span></span>, que corresponde al cuociente (división) de dos funciones, por lo tanto, debemos aplicar la regla de la derivada de la división de dos funciones:</span></span></font></p> <p align="justify"><font style="font-style: italic" 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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«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»</span></span></span></span></span></span></span></span></span></span></span></font></p> <p align="justify"><font style="font-style: italic" size="4"><span style="font-family: times new roman,times,serif"><span class="nolink"></span><br /></span></font><font style="font-style: italic" size="4"><span style="font-family: times new roman,times,serif"><br /></span></font><font style="font-style: italic" size="4"><br style="font-family: times new roman,times,serif" /></font><font style="font-style: italic" size="4"><span style="font-family: times new roman,times,serif"></span></font><font style="font-style: italic; font-family: times new roman,times,serif" size="4">Para el caso particular de </font><font style="font-style: italic; font-family: times new roman,times,serif" size="4">f(#x)=<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»#g«/mi»«/mrow»«mrow»«mi»#h«/mi»«/mrow»«/mfrac»«/math»</span></span></span></span></span></span></span></span></font><span style="font-style: italic; font-family: times new roman,times,serif"></span><font style="font-style: italic; font-family: times new roman,times,serif" size="4">,</font><font style="font-style: italic; font-family: times new roman,times,serif" size="4"><font size="4"> su derivada queda:</font></font><br style="font-family: times new roman,times,serif" /><span class="nolink"><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¨»«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»</span></span></span></span></span></span></span></span></span><br /><br /><span style="font-style: italic; font-family: times new roman,times,serif"><font size="4">Luego, </font></span><br /><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">«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»</span></span></span></span></span></span></span></span></span><br /><br /><br /><font size="4"><span style="font-style: italic; font-family: times new roman,times,serif"></span></font><br /><br /><br /></p><br /><br />
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Answer 1
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<font size="4"><span style="font-style: italic; font-family: times new roman,times,serif">Bien. Continúa de esa manera.</span></font>
Answer 2
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<p align="justify"><font size="4" face="times new roman,times,serif"><em>Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</em></font></p>
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66.66667%
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33.33333%
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16.66667%
14.28571%
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11.11111%
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