document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112736>Question 1112736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Let f(t)=(t^2+6t+4)(2t^2+5)<BR>\n" );
document.write( "f'(t)=<BR>\n" );
document.write( "f'(2)=\r<BR>\n" );
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document.write( "2) f(x)=4x / &#8730;8x2+5x&#8722;5.\r<BR>\n" );
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document.write( " Evaluate f&#8242;(x) at x=2\r<BR>\n" );
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document.write( "f&#8242;(2) =<BR>\n" );
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document.write( "3) Suppose that y=5(x2+6x)&#8722;1.\r<BR>\n" );
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document.write( "Find dy / dx =\r<BR>\n" );
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document.write( "4) Find f&#8242;(x) if <BR>\n" );
document.write( "f(x)=(4x&#8722;4)^2&#8901;(3x^2+7)^2.\r<BR>\n" );
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document.write( "5) Differentiate y=(x^2+5 / x^2&#8722;5)^2.<BR>\n" );
document.write( "dy / dx=\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727791 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=727791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "One problem per post.\r<BR>\n" );
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document.write( "5.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{d}{dx}\ \[\frac{\(x^2\ +\ 5\)^2}{\(x^2\ -\ 5\)^2}\] \">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large u\ =\ x^2\ +\ 5\"> and let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large v\ =\ x^2\ -\ 5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{d}{dx}\ \[\frac{u^2}{v^2}\]\ =\ \frac{\frac{d}{dx}u^2\cdot v^2\ -\ u^2\cdot \frac{d}{dx}v^2}{v^4}\">\r<BR>\n" );
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document.write( "By the quotient rule\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ =\ \frac{2u\frac{du}{dx}\cdot v^2\ -\ 2v\frac{dv}{dx}\cdot u^2}{v^4}\">\r<BR>\n" );
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document.write( "By the chain rule\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{du}{dx}\ =\ \frac{dv}{dx}\ =\ 2x\">\r<BR>\n" );
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document.write( "So substituting back:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{4x\(x^2\ +\ 5\)\(x^2\ -\ 5\)^2\ -\ 4x\(x^2\ -\ 5\)\(x^2\ +\ 5\)^2}{\(x^2\ -\ 5\)^4\">\r<BR>\n" );
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document.write( "A little more algebra...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{d}{dx}\ \[\frac{\(x^2\ +\ 5\)^2}{\(x^2\ -\ 5\)^2}\]\ =\ -\frac{40\(x^2\ +\ 5\)}{\(x^\ -\ 5\)^3}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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