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<span style="color: rgb(0, 0, 0); font-family: arial,sans,sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; display: inline ! important; float: none;"></span><span style="font-style: italic;"><font size="4"><span style="font-family: 'times new roman',times,serif;">Si <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»F«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#F1«/mi»«/math»</span>. <br />Entonces, <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»F«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»</span> <br /></span></font></span>
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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;">Solución:<br /><br />Podemos ver que la función <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»F«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«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»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f1«/mi»«/math»</span> y <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#g1«/mi»«/math»</span>, podemos reescribir <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»F«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»</span> de la siguiente forma:<br /></span></span></font> <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¨»«mi»F«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#F1«/mi»«mo»=«/mo»«mi»#F2«/mi»«mo»=«/mo»«mi»f«/mi»«mfenced»«mrow»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mfenced»«mrow»«mi»f«/mi»«mo»§#8728;«/mo»«mi»g«/mi»«/mrow»«/mfenced»«mfenced»«mi»x«/mi»«/mfenced»«/math»</span></span></span></font><br /><br /><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"></span></span></font></div><font size="4"><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»f«/mi»«mo»(«/mo»«mi»x«/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»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»</span> <span style="font-family: 'times new roman',times,serif; font-style: italic;">son dos funciones; entonces,</span> <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»f«/mi»«mo»§#8728;«/mo»«mi»g«/mi»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«/math»</span></span></span> -<span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;">utilizando la regla de la cadena sobre la composición de dos funciones- está dada por la derivada de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»</span> evaluada en <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»</span>, multiplicada por la derivada de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»</span>, es decir:<br /></span></span></font> <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»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi»f«/mi»«mo»§#8728;«/mo»«mi»g«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfenced»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mrow»«/mfrac»«mfenced»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»·«/mo»«mfenced»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/math»</span><br /><br /></span></span><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"></span></span></font></div><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><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»f«/mi»«mo»(«/mo»«mi»x«/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»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#g1«/mi»«/math»</span> .<br /><br />Primero, la derivada de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»</span> está dada por:</span></span></span></span></font><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><br /></span></span></span></span> <div align="center"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><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»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#df«/mi»«/math»</span> </span></span></span></span><br /><br /></div> <div style="text-align: center;"><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"></span></span></span></span></font></div><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><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»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»</span>, obtenemos:</span></span></span></span></font><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><br /></span></span></span></span> <div align="center"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><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»f«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«/math»</span><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mi»#dfg«/mi»«/math»</span>.</span></span></span></span><br /><br /></div> <div style="text-align: center;"><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"></span></span></span></span></font></div><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><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»g«/mi»«/math»</span>.<br /></span></span></span></span></font> <div style="text-align: center;"><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><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»g«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#dg«/mi»«/math»</span>.<br /><br /></span></span></span></span><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"></span></span></span></span></font></div><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;">De lo anterior se tiene que:<br /></span></span></span></span></font> <div align="center"><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><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»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mi»x«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mi»d«/mi»«mfenced»«mrow»«mi»f«/mi»«mo»§#8728;«/mo»«mi»g«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mi»x«/mi»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfenced»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»·«/mo»«mfenced»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfenced»«mrow»«mi»#dfg«/mi»«/mrow»«/mfenced»«mo»·«/mo»«mfenced»«mrow»«mi»#dg«/mi»«/mrow»«/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></span></span></font><br /><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"></span></span></span></span></font></div><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;">Por lo tanto:<br /></span></span></span></span></font> <div style="text-align: center;"><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><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»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»#F1«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»#d«/mi»«/math»</span></span></span></span></span><br /><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"></span></span></span></span></font></div><font size="4"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"><span style="font-style: italic;"><span style="font-family: 'times new roman',times,serif;"></span></span></span></span></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;"><span style="font-style: italic;"><span style="font-style: italic;"><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><br /></span></span></div> <div style="text-align: justify; font-family: 'times new roman',times,serif; font-style: italic;"><font size="4"><b id="internal-source-marker_0.9600851237773895" style="color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; font-weight: normal;"> <p dir="ltr" style="margin-left: 36pt; margin-top: 0pt; margin-bottom: 0pt;"><span style="font-size: 15px; color: rgb(0, 0, 0); font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p></b></font></div>
Answer 2
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None
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66.66667%
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<div style="text-align: justify; font-family: 'times new roman',times,serif; font-style: italic;"><font size="4"><b id="internal-source-marker_0.9600851237773895" style="color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; font-weight: normal;"><span style="font-size: 15px; color: rgb(0, 0, 0); font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><font size="4"><span style="font-style: italic;">Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</span></font><br /><br /></span></b></font></div>
Answer 3
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66.66667%
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14.28571%
12.5%
11.11111%
10%
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