document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201323>Question 1201323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can someone help me with this question please? I'm trying hard to put the formula the correct way but I'm not sure\r<BR>\n" );
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document.write( "w(x)=(e^x-11 ln⁡x+340x^5)/(7x^3-32e^x+5 ln⁡x )\r<BR>\n" );
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document.write( "What's the rule and what are three steps that can be applied when differentiating? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835629 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Whenever dealing with complicated formulas, it helps to break things up into smaller pieces.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w(\text{x}) = \frac{f(\text{x})}{g(\text{x})}\"><BR>\n" );
document.write( "where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(\text{x}) = e^{\text{x}}-11\ln(\text{x})+340\text{x}^5\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g(\text{x}) = 7\text{x}^3-32e^{\text{x}}+5\ln(\text{x})\">\r<BR>\n" );
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document.write( "We'll need the derivatives of the functions f(x) and g(x) separately.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f'(\text{x}) = e^{\text{x}}-\frac{11}{\text{x}}+1700\text{x}^4\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g'(\text{x}) = 21\text{x}^2-32e^{\text{x}}+\frac{5}{\text{x}}\"><BR>\n" );
document.write( "Let me know if you need me to go over the derivative rules.\r<BR>\n" );
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document.write( "I'll rewrite each fraction of the form a/b into ab^(-1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f'(\text{x}) = e^{\text{x}}-11\text{x}^{-1}+1700\text{x}^4\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g'(\text{x}) = 21\text{x}^2-32e^{\text{x}}+5\text{x}^{-1}\">\r<BR>\n" );
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document.write( "Use the quotient rule to apply the derivative to w(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w(\text{x}) = \frac{f(\text{x})}{g(\text{x})}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w'(\text{x}) = \frac{f'(\text{x})g(\text{x}) - f(\text{x})g'(\text{x})}{(g(\text{x}))^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w'(\text{x}) = \frac{(e^{\text{x}}-11\text{x}^{-1}+1700\text{x}^4)(7\text{x}^3-32e^{\text{x}}+5\ln(\text{x}))-(e^{\text{x}}-11\ln(\text{x})+340\text{x}^5)(21\text{x}^2-32e^{\text{x}}+5\text{x}^{-1})}{(7\text{x}^3-32e^{\text{x}}+5\ln(\text{x}))^2}\">\r<BR>\n" );
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document.write( "Things spiral out of hand by the third step.<BR>\n" );
document.write( "You can optionally expand things out and combine like terms. <BR>\n" );
document.write( "But it's probably better to leave it as it is.<BR>\n" );
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