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<p style="font-family: 'times new roman',times,serif; font-style: italic; text-align: justify;"><font size="4">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">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f«/mi»«mo»(«/mo»«mi»#k«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>. <br /></font></p> <p style="font-family: 'times new roman',times,serif; font-style: italic; text-align: justify;"><font size="4">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">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f«/mi»«mfenced»«mrow»«mi»#k«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#k«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></font></p>
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<p style="text-align: justify;"><span class="nolink"></span><font size="4" face="times new roman,times,serif"><em>Solución:</em></font></p> <p style="text-align: justify;"><font size="4" face="times new roman,times,serif"><em>Para resolver, aplicamos álgebra de derivadas. En este caso, haremos uso de las siguientes propiedades:</em></font></p> <p style="text-align: justify;"><font size="4" face="times new roman,times,serif"><em> <table width="100%" cellspacing="10" cellpadding="10" border="1" align="middle" rules="none" frame="void" style="background-image: none; float: none; text-align: center; vertical-align: middle; border-style: none;"><tbody> <tr> <td width="90%" valign="top" 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»#x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»p«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/mfenced»«mo»±«/mo»«mi»q«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»p«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»±«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»q«/mi»«mfenced»«mrow»«mi»#x«/mi»«/mrow»«/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="90%" valign="top" 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¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mfenced»«msup»«mi»#x«/mi»«mi»m«/mi»«/msup»«/mfenced»«mo»=«/mo»«mi»m«/mi»«mo»·«/mo»«msup»«mi»#x«/mi»«mrow»«mi»m«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«/mtable»«/math»</span><br /> </td> <td width="10%" valign="top" style="background-image: none; text-align: center; vertical-align: middle; border-style: none;">(2)<br /> </td> </tr></tbody> </table></em></font></p> <p style="text-align: justify;"><font size="4" face="times new roman,times,serif"><em>Aplicando la propiedad </em>(1)<em> se obtiene:<br /></em></font></p> <p style="text-align: justify;"><font face="times new roman,times,serif"><font size="4"><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">«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»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«mi»#r1«/mi»«mo»)«/mo»«mi»#s2«/mi»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n22«/mi»«mi»#r2«/mi»«mo»)«/mo»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> </em></font></font></p> <p style="text-align: justify;"><font size="4" face="times new roman,times,serif"><em>Escribiendo cada raíz en forma de potencia</em> <em>se obtiene:<br /></em></font></p> <p style="text-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"><font size="4" face="times new roman,times,serif"><span class="nolink"><em><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»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n1«/mi»«msup»«mi»#x«/mi»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«/msup»«mo»)«/mo»«mi»#s2«/mi»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»#x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#n22«/mi»«msup»«mi»#x«/mi»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«/msup»«mo»)«/mo»«/math»</span></span></em></span></font></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-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"><font size="4" face="times new roman,times,serif"><span class="nolink"><em>Aplicando la propiedad (2)</em>:<em><br /></em></span></font></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-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"><font size="4" face="times new roman,times,serif"><span class="nolink"><em><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»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#n1«/mi»«mo»·«/mo»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«msup»«mi»#x«/mi»«mrow»«mfrac»«mi»#e1«/mi»«mi»#i1«/mi»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mi»#s1«/mi»«mi»#n2«/mi»«mo»·«/mo»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«msup»«mi»#x«/mi»«mrow»«mfrac»«mi»#e2«/mi»«mi»#i2«/mi»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»</span></span></em></span></font></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: justify;"><font size="4" face="times new roman,times,serif"><i>Reduciendo:</i></font><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"><font size="4" face="times new roman,times,serif"><span class="nolink"><em><span class="nolink"></span></em></span></font></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-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"><font size="4" face="times new roman,times,serif"><span class="nolink"><em><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»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#n3«/mi»«msup»«mi»#x«/mi»«mi»#e3«/mi»«/msup»«mi»#s1«/mi»«mi»#n4«/mi»«msup»«mi»#x«/mi»«mi»#e4«/mi»«/msup»«/math»</span></span></em></span></font></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: justify;"><font size="4"><i><font face="times new roman,times,serif">Reescribiendo como raíz </font></i></font><font size="4"><i><font face="times new roman,times,serif">se tiene</font></i></font>:<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"><font size="4" face="times new roman,times,serif"><span class="nolink"><em><span class="nolink"></span></em></span></font></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: justify;"><span class="nolink"><font size="4" face="times new roman,times,serif"><em></em></font></span></p> <p style="text-align: justify;"><span class="nolink"><font size="4" face="times new roman,times,serif"><em></em></font></span></p> <p style="text-align: justify;"><span class="nolink"><font size="4" face="times new roman,times,serif"><em></em></font></span></p> <p style="text-align: justify;"><span class="nolink"><font size="4" face="times new roman,times,serif"><em></em></font></span></p> <p style="text-align: justify;"><font size="4" face="times new roman,times,serif"><em></em></font></p> <p style="text-align: justify;"><font size="4" face="times new roman,times,serif"><em></em></font></p> <p style="text-align: justify;"><span class="nolink"><font size="4" face="times new roman,times,serif"><span class="nolink"><em><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»#r1«/mi»«mi»#s1«/mi»«mi»#n2«/mi»«mi»#r2«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#n3«/mi»«mi»#u«/mi»«mi»#s1«/mi»«mi»#n4«/mi»«mi»#v«/mi»«/math»</span></span></em></span></font></span></p>
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<span style="background-color: transparent; font-variant: normal; font-style: italic; font-family: arial; white-space: pre-wrap; color: rgb(0, 0, 0); font-size: 15px; vertical-align: baseline; font-weight: normal; text-decoration: none;"><font size="4" face="times new roman,times,serif">¡Muy bien! Sigue así.</font></span>
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<p><em><font size="4" face="times new roman,times,serif">Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</font></em></p>
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