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<font size="4" style="font-style: italic; font-family: times new roman,times,serif;">Si <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»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mi»#a1«/mi»«mi»#tri«/mi»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/math»</span></span></span></span></span></span></span></span>. Entonces, <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»f«/mi»«mo»(«/mo»«mi»#v«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»</span></span></span></span></span></span></span></span><br /></font> <div style="text-align: center; font-style: italic; font-family: times new roman,times,serif;"><font size="4"><br /></font></div><font size="4" style="font-style: italic; font-family: times new roman,times,serif;"> <p align="justify"><font color="#990000">Obs.:</font></p> <p align="justify"><font color="#990000">Ingresa las funciones trigonométricas de la siguiente manera:</font></p> <p align="justify"><font color="#990000">1. seno(x) se ingresa sen(x)</font></p> <p align="justify"><font color="#990000">2. coseno(x) se ingresa cos(x)</font><br /></p></font><font size="4"> <div style="text-align: center; font-style: italic; font-family: times new roman,times,serif;"><br /></div></font>
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<font size="4" style="font-style: italic; font-family: times new roman,times,serif;">Solución:<br /><br />Recuerda que la derivada de la multiplicación de dos funciones se desarrolla de la siguiente manera:<br /><br /><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Si:</span><br style="font-family: times new roman,times,serif;" /></font></font> <div style="text-align: center;"><font size="4" style="font-style: italic; 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»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»g«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi»h«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span></font><font size="4" style="font-style: italic;"><br /><br style="font-family: times new roman,times,serif;" /></font> <div style="text-align: left;"><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Entonces, la derivada de la multiplicación de estas dos funciones es:</span></font><br /></div><br /></div> <div style="text-align: center;"><font size="4" style="font-style: italic; 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">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»g«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi»h«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»+«/mo»«mi»g«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»h«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span></span></span></span></font><font size="4" style="font-style: italic;"><br style="font-family: times new roman,times,serif;" /><br style="font-family: times new roman,times,serif;" /></font> <div style="text-align: left; font-style: italic; font-family: times new roman,times,serif;"><font size="4">Con lo anterior, se puede separar <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»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mi»#a1«/mi»«mi»#tri«/mi»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/math»</span></span></span></span></span></span></span></span> de la siguiente forma:<br /></font> <div style="text-align: center;"><font size="4"><br /></font></div></div> <div style="text-align: center;"><font size="4" style="font-style: italic; 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»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»g«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi»h«/mi»«mfenced»«mrow»«mi»#v«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span><br /></font> <div style="text-align: left;"><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Con:</span><br style="font-family: times new roman,times,serif;" /></font> <div style="text-align: center;"><font size="4" style="font-style: italic;"><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»«mtr»«mtd»«mi»g«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a1«/mi»«mi»#tri«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»h«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mtd»«/mtr»«/mtable»«/math»</span></span></span></span></span></span></span></span><br style="font-family: times new roman,times,serif;" /><font size="4"><br style="font-family: times new roman,times,serif;" /></font></font> <div style="text-align: left;"><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">A<span style="font-style: italic; font-family: times new roman,times,serif;">sí</span></span></font><font size="4">,<br style="font-style: italic; font-family: times new roman,times,serif;" /><br style="font-style: italic; font-family: times new roman,times,serif;" /></font> <div style="text-align: center;"><font size="4"><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»#v«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«mo»=«/mo»«mfenced»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»#a1«/mi»«mi»#tri«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«mo»+«/mo»«mi»#a1«/mi»«mi»#tri«/mi»«mo»·«/mo»«mfenced»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mrow»«/mfenced»«/mrow»«/mfenced»«/math»</span></span></span></span></span></span></span></span><br style="font-style: italic; font-family: times new roman,times,serif;" /><br style="font-style: italic; font-family: times new roman,times,serif;" /></font> <div style="text-align: justify;"><font size="4"><span style="font-style: italic; font-family: times new roman,times,serif;">Ahora procedemos a derivar las funciones anteriores:</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"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»#a1«/mi»«mi»#tri«/mi»«mo»=«/mo»«mi»#t1«/mi»«/math»</span></span></span></span></span></span></span></span><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">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«mo»=«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/math»</span></span></span></span></span></span></span></span><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">, ya que la derivada de la función </span><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¨»«msup»«mi»e«/mi»«mrow»«mi»#v«/mi»«/mrow»«/msup»«/math»</span></span></span></span></span></span></span></span><span style="font-family: times new roman,times,serif;"> es la misma función.</span></font><br /><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;"></span></font><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;"></span></font><br /><br /><font size="4"><br style="font-family: times new roman,times,serif;" /><span style="font-style: italic; font-family: times new roman,times,serif;">Por lo tanto,</span></font><br /> <div style="text-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">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mtable»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#v«/mi»«/mrow»«/mfrac»«mi»f«/mi»«mfenced»«mi»#v«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#t1«/mi»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«mo»+«/mo»«mi»#a1«/mi»«mi»#tri«/mi»«mo»·«/mo»«mi»#a2«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a6«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«mo»+«/mo»«mi»#a3«/mi»«mi»#tri«/mi»«msup»«mi»#e«/mi»«mi»#v«/mi»«/msup»«/mtd»«/mtr»«/mtable»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»</span></span></span></span></span></span></span></span><br /></div></div><br /></div></div></div></div></div></div>
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<font size="4"><span style="font-style: italic; font-family: times new roman,times,serif;">¡Muy bien! Sigue así.</span></font>
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<font size="4" style="font-style: italic; font-family: times new roman,times,serif;">Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</font>
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