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<font size="4"><i><font face="times new roman,times,serif">Si</font><font face="times new roman,times,serif"> <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»F«/mi»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»#F1«/mi»«/math»</span></font><font face="times new roman,times,serif">. Entonces, <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»F«/mi»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»</span></font></i></font><br />
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<div align="justify"><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">Solución:<br /><br />Podemos ver que la función <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»F«/mi»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»#F1«/mi»«/math»</span> corresponde a la composición de las funciones <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f1«/mi»«/math»</span> y <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#g1«/mi»«/math»</span>. <br />Por lo tanto, definiendo <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f2«/mi»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»#f1«/mi»«/math»</span> y <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#k«/mi»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»#g1«/mi»«/math»</span> podemos reescribir <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»F«/mi»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«/math»</span> de la siguiente forma:</span></span></font><br /><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><br /></span></span></font> <div align="center"><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»F«/mi»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»#F1«/mi»«mo»=«/mo»«mi»#F2«/mi»«mo»=«/mo»«mi»#f2«/mi»«mfenced»«mrow»«mi»#k«/mi»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mfenced»«mrow»«mi»#f2«/mi»«mo»§#8728;«/mo»«mi»#k«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mi»#var«/mi»«/mrow»«/mfenced»«/math»</span></span></span></font><br /><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><br /></span></span></font> <div align="justify"><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">Recordemos que si <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f2«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/math»</span></span></span> <span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">y</span></span> <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/math»</span> <span style="font-family: 'times new roman', times, serif; font-style: italic; ">son dos funciones; entonces</span><font face="times new roman,times,serif">,</font> <span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">la derivada de la compuesta <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»#f2«/mi»«mo»§#8728;«/mo»«mi»#k«/mi»«mo»)«/mo»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f2«/mi»«mo»(«/mo»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«mo»)«/mo»«/math»</span></span></span> <span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">está dada por la derivada de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f2«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/math»</span> evaluada en <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/math»</span>, multiplicada por la derivada de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/math»</span>; es decir:</span></span></font><br /><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><br /></span></span></font><span style="text-align: justify; "></span> <div style="text-align: center; "> <div align="center"><font size="4"><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»F«/mi»«mfenced»«mi»#var«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»#f2«/mi»«mo»§#8728;«/mo»«mi»#k«/mi»«mo»)«/mo»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfenced»«mfrac»«mrow»«mi»d«/mi»«mi»#f2«/mi»«mfenced»«mrow»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mrow»«/mfrac»«/mfenced»«mo»·«/mo»«mfenced»«mfrac»«mrow»«mi»d«/mi»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«/mfenced»«/math»</span></span></span></font><br /></div><font size="4"><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><br /></span></span></font> <div align="justify"><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">Ahora, necesitamos determinar la derivada de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f2«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f1«/mi»«/math»</span> evaluada en <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#g1«/mi»«/math»</span>.</span></span></font><br /><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><br />Primero, la derivada de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f2«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/math»</span> está dada por:<br /></span></span></font><span style="text-align: justify; "></span> <div style="text-align: center; "><font size="4"><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#f2«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#df«/mi»«/math»</span> </span></span><br /><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">Luego, evaluando en <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/math»</span> obtenemos:<br /></span></span></font><span style="text-align: justify; "></span> <div style="text-align: center; "><font size="4"><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mo»§nbsp;«/mo»«mi»#f2«/mi»«mo»(«/mo»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«/math»</span><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mi»#dfg«/mi»«/math»</span>.</span></span><br /><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">Por otra parte, nos falta calcular la derivada de la función <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#k«/mi»«/math»</span>.<br />Así:<br /></span></span></font><span style="text-align: justify; "></span> <div style="text-align: center; "><font size="4"><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»#k«/mi»«mo»(«/mo»«mi»#var«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#dg«/mi»«/math»</span>.</span></span><br /><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">De lo anterior se tiene que:<br /><br /></span></span></font> <div align="center"><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»F«/mi»«mfenced»«mi»#var«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mi»d«/mi»«mfenced»«mrow»«mi»#f2«/mi»«mo»§#8728;«/mo»«mi»#k«/mi»«/mrow»«/mfenced»«mfenced»«mi»#var«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfenced»«mfrac»«mrow»«mi»d«/mi»«mo»§nbsp;«/mo»«mi»#f2«/mi»«mfenced»«mrow»«mi»#k«/mi»«mfenced»«mi»#var«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«/mfenced»«mo»·«/mo»«mfenced»«mfrac»«mrow»«mi»d«/mi»«mo»§nbsp;«/mo»«mi»#k«/mi»«mfenced»«mi»#var«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#dfg«/mi»«mo»·«/mo»«mfenced»«mi»#dg«/mi»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#d«/mi»«/mtd»«/mtr»«/mtable»«/math»</span></span></span></font><br /><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "></span></span></font></div><font size="4" style="text-align: justify; "><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">Por lo tanto:<br /></span></span></font><span style="text-align: justify; "></span> <div style="text-align: center; "><font size="4"><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; "><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»F«/mi»«mfenced»«mi»#var«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mfenced»«mi»#F1«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#var«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#d«/mi»«/math»</span></span></span></font><font size="4" style="text-align: justify; "><br class="Apple-interchange-newline" /></font></div>
No, case is unimportant
Yes, case must match
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Answer 1
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<div style="text-align: justify; "><font size="4"><span style="font-style: italic; "><span style="font-family: 'times new roman', times, serif; ">Bien. Continúa de esa manera.</span></span></font></div> <div style="text-align: justify; font-family: 'times new roman', times, serif; font-style: italic; "> <div><font size="4"><b id="internal-source-marker_0.9600851237773895" style="font-style: normal; font-size: medium; font-weight: normal; "><br class="Apple-interchange-newline" /></b></font></div></div>
Answer 2
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None
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90%
83.33333%
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70%
66.66667%
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40%
33.33333%
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20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
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<font size="4"><b id="internal-source-marker_0.9600851237773895" style="font-family: 'times new roman', times, serif; text-align: justify; font-weight: normal; "><span style="vertical-align: baseline; white-space: pre-wrap; "><span style="font-style: italic; ">Revisa </span></span></b><span style="font-family: 'times new roman', times, serif; text-align: justify; font-weight: normal; "><span style="vertical-align: baseline; white-space: pre-wrap; "><span style="font-style: italic; "><font face="times new roman,times,serif">el</font></span></span></span><b id="internal-source-marker_0.9600851237773895" style="font-family: 'times new roman', times, serif; text-align: justify; font-weight: normal; "><span style="vertical-align: baseline; white-space: pre-wrap; "><span style="font-style: italic; "> desarrollo para identificar tus errores. ¡Tú puedes!</span></span></b></font>
Answer 3
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66.66667%
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33.33333%
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25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
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