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<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">«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>.</em></font></p> <p align="justify"><font size="4" face="times new roman,times,serif"><em>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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><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»«/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></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 size="4" face="times new roman,times,serif" color="#990000"><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 size="4" face="times new roman,times,serif" color="#990000"><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 size="4" face="times new roman,times,serif" color="#990000"><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 size="4" face="times new roman,times,serif" color="#990000"><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 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>
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<p align="justify" style="font-family: times new roman,times,serif;"><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>Para calcular 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">«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></em><em> , aplicaremos álgebra de derivadas. En particular, 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 width="100%" cellspacing="10" cellpadding="10" border="1" style="background-image: none; float: none; text-align: center; vertical-align: middle; border-style: none;" frame="void" rules="none"><tbody> <tr> <td width="33%" valign="top" align="center" rowspan="1" colspan="2" style="background-image: none; text-align: center; vertical-align: middle; border-style: none;"><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><br /> </td> <td width="10%" valign="top" style="background-image: none; text-align: center; vertical-align: middle; border-style: none;">(1)<br /> </td> </tr> <tr> <td width="33%" valign="top" align="center" rowspan="1" colspan="2" style="background-image: none; text-align: center; vertical-align: middle; border-style: none;"><em><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></em> </td> <td width="10%" valign="top" rowspan="1" style="background-image: none; text-align: center; vertical-align: middle; border-style: none;">(2)<br /> </td> </tr> <tr> <td width="45%" valign="top" align="center" style="background-image: none; text-align: center; vertical-align: middle; border-style: none;"><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><br /> </td> <td width="45%" valign="top" align="center" style="background-image: none; text-align: center; vertical-align: middle; border-style: none;"><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><br /> </td> <td width="10%" valign="top" rowspan="1" colspan="1" style="background-image: none; text-align: center; vertical-align: middle; border-style: none;">(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 width="100%" border="0" rules="none" frame="void" style="background-image: none; float: none; text-align: center; vertical-align: middle; border-style: none;"><tbody> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;"><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><br /> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: bottom; border-style: none;"> <blockquote>/ Ocupando la identidad <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> tenemos: </blockquote> </td> </tr> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;"><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><br /> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: middle; border-style: none;"> <blockquote>/ Ocupando (2),tenemos:<br /></blockquote> </td> </tr> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;" rowspan="1"><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><br /> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: middle; border-style: none;" rowspan="1"> <blockquote>/ Ocupando la propiedad (3) enunciada al inicio de la resolución, tenemos:<br /></blockquote> </td> </tr> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;" rowspan="1"><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><br /> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: middle; border-style: none;" rowspan="1"> <blockquote>/ Desarrollando los productos del numerador:<br /></blockquote> </td> </tr> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;" rowspan="1"><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><br /> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: middle; border-style: none;" rowspan="1"> <blockquote>/ Separando en suma de dos fracciones:<br /></blockquote> </td> </tr> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;" rowspan="1"><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><br /> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: middle; border-style: none;" rowspan="1"> <blockquote>/ Ocupando <em><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></em>, se obtiene finalmente:<br /></blockquote> </td> </tr> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;" rowspan="1"><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><br /> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: middle; border-style: none;" rowspan="1"><br /> </td> </tr> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;" rowspan="1"><br /> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: middle; border-style: none;" rowspan="1"><br /> </td> </tr> <tr> <td width="50%" valign="top" align="right" style="background-image: none; text-align: right; vertical-align: middle; border-style: none;" rowspan="1"> <blockquote>Por lo tanto,<br /></blockquote> </td> <td width="50%" valign="top" style="background-image: none; text-align: left; vertical-align: middle; border-style: none;" rowspan="1"> <blockquote><br /><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> (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 align="justify" style="font-family: times new roman,times,serif;"><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">«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></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¨»«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></i></font></p> <p align="justify" style="font-family: times new roman,times,serif;"><font size="4"><i>Ocupando las propiedades (3) y (4) obtenemos:</i></font></p> <p align="justify" style="font-family: times new roman,times,serif;"><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 align="justify" style="font-family: times new roman,times,serif;"><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">«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></em></i></font><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></i></font></p> <p align="justify" style="font-family: times new roman,times,serif;"><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 align="justify" style="font-family: times new roman,times,serif;"><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">«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></i></font></p> <p align="justify" style="font-family: times new roman,times,serif;"><font size="4"><i>Por lo tanto:<br /></i></font></p> <p style="text-align: center; font-family: times new roman,times,serif;"><font size="4"><i><font 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 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></em></font></i></font></p> <p align="justify" style="font-style: italic; font-family: times new roman,times,serif;"><font size="4"><span class="nolink"><em><span class="nolink"><span class="nolink"></span></span></em></span></font></p> <p align="justify" style="font-style: italic; font-family: times new roman,times,serif;"></p> <p align="justify" style="font-style: italic; font-family: times new roman,times,serif;"></p> <p></p>
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