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<div align="justify" style="text-align: justify;"><font size="3" style="font-style: italic;"><span style="font-family: times new roman,times,serif;"><font size="4">Si</font> </span><span style="font-family: times new roman,times,serif;"></span></font><font size="3"><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»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math»</span></span></span></span></span></span></span></span></span></span>. E</span><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">ntonces, </span></font></font><font size="3"><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»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»</span></span></span></span></span></span></span></span></span></span></span></font></div> <div align="justify" style="text-align: justify;"><font size="3"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span><br /></font> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em>Obs.: Ingresa las funciones trigonométricas de las siguiente manera:</em></font></div> <div align="justify" style="text-align: justify;"><em><font size="4" face="Times New Roman" color="#990000"></font></em></div> <div align="justify" style="text-align: justify;"><em><font size="4" face="Times New Roman" color="#990000"></font></em></div> <div align="justify" style="text-align: justify;"></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em>- seno(x) se ingresa sen(x)</em></font></div> <div align="justify" style="text-align: justify;"><em><font size="4" face="Times New Roman" color="#990000"></font></em></div> <div align="justify" style="text-align: justify;"><em><font size="4" face="Times New Roman" color="#990000"></font></em></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em>- coseno(x) se ingresa cos(x)</em></font></div> <div align="justify" style="text-align: justify;"><em><font size="4" face="Times New Roman" color="#990000"></font></em></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em></em></font></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em>- tangente(x) se ingresa tan(x)</em></font></div> <div align="justify" style="text-align: justify;"><em><font size="4" face="Times New Roman" color="#990000"></font></em></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em></em></font></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em>- cosecante(x) se ingresa cosec(x)</em></font></div> <div align="justify" style="text-align: justify;"><em><font size="4" face="Times New Roman" color="#990000"></font></em></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em></em></font></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em>- secante(x) se ingresa sec(x)</em></font></div> <div align="justify" style="text-align: justify;"></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em></em></font></div> <div align="justify" style="text-align: justify;"><font size="4" face="times new roman,times,serif" color="#990000"><em>- cotangente(x) se ingresa cotan(x)</em></font></div> <div align="justify" style="text-align: justify;"><font size="3"></font></div></div>
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<div style="text-align: justify;"><font size="4"><span style="font-style: italic; font-family: times new roman,times,serif;">Solución: </span><br style="font-style: italic; font-family: times new roman,times,serif;" /><br /></font><font size="4"> <div style="text-align: justify;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><font face="times new roman,times,serif"><em>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">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#exr1«/mi»«/math»</span></span></span></span></span></span></span></span> corresponde a un cuociente de funciones, por lo tanto, aplicaremos la regla de la derivada para el cuociente (división) de funciones:</em></font></span></span></span></span></div> <div style="text-align: justify;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><em><font face="Times New Roman"></font></em></span></span></span></span></div> <div style="text-align: justify;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></div> <div style="text-align: justify;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></div> <div style="text-align: justify;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><em><font face="Times New Roman"></font></em></span></span></span></span></div> <div style="text-align: justify;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><em><font face="Times New Roman"></font></em></span></span></span></span></div><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span></font></div> <div style="text-align: justify;"><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"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mfrac»«mrow»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»-«/mo»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/mrow»«msup»«mfenced»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mo»§nbsp;«/mo»«mo»,«/mo»«mo»§nbsp;«/mo»«mo»§#8704;«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§nbsp;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#8800;«/mo»«mn»0«/mn»«/math»</span></span></span></span></span></span></span></span></span></span></span></font></div> <div align="justify" style="text-align: justify;"><font size="4"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><font face="times new roman,times,serif"><em>En nuestro caso:</em></font></span></span></span></span></span></font></div> <div style="text-align: justify;"><br 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"><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»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr3«/mi»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»A«/mi»«mi»p«/mi»«mi»l«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§nbsp;«/mo»«mi»á«/mi»«mi»l«/mi»«mi»g«/mi»«mi»e«/mi»«mi»b«/mi»«mi»r«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»v«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»v«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»c«/mi»«mi»i«/mi»«mi»ó«/mi»«mi»n«/mi»«mo»§nbsp;«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mi»g«/mi»«mi»o«/mi»«mi»n«/mi»«mi»o«/mi»«mi»m«/mi»«mi»é«/mi»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mo»:«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr4«/mi»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»A«/mi»«mi»p«/mi»«mi»l«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»v«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»t«/mi»«mi»e«/mi»«mi»n«/mi»«mi»c«/mi»«mi»i«/mi»«mi»a«/mi»«mo»:«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr5«/mi»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»A«/mi»«mi»l«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»s«/mi»«mi»a«/mi»«mi»r«/mi»«mi»r«/mi»«mi»o«/mi»«mi»l«/mi»«mi»l«/mi»«mi»a«/mi»«mi»r«/mi»«mo»§nbsp;«/mo»«mi»l«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mi»m«/mi»«mi»u«/mi»«mi»l«/mi»«mi»t«/mi»«mi»i«/mi»«mi»p«/mi»«mi»l«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mi»c«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»o«/mi»«mi»r«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»l«/mi»«mo»§nbsp;«/mo»«mi»p«/mi»«mi»r«/mi»«mi»i«/mi»«mi»m«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§nbsp;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»s«/mi»«mi»i«/mi»«mi»s«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»s«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»o«/mi»«mi»b«/mi»«mi»t«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»e«/mi»«mo»:«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr6«/mi»«/mtd»«/mtr»«/mtable»«/math»</span></span></span></span></span></span></span></span></span></span></span><br /><br /><font size="4"><span style="font-style: italic; font-family: times new roman,times,serif;">Por lo tanto,</span></font></div> <div style="text-align: justify;"><font size="4"><span style="font-style: italic; font-family: times new roman,times,serif;"></span></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">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#exr6«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span><br /><br /></div> <div style="text-align: justify;"></div>
No, case is unimportant
Yes, case must match
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<div style="text-align: justify; font-style: italic;"><font size="4"><span style="font-family: times new roman,times,serif;">¡Muy Bien! Sigue asÃ.</span></font></div>
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<font size="4" face="times new roman,times,serif"><em>Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</em></font>
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