document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248534>Question 248534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need the derivative of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282x%5E2-10%29%2F%28x%5E2%2B5%29%5E2+ ALIGN=MIDDLE  ALT=\"+%282x%5E2-10%29%2F%28x%5E2%2B5%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "i came up with a final answer of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%2A%28-x%5E4%2B10x%5E2%2B75%29%2F%28x%5E2%2B5%29%5E4+ ALIGN=MIDDLE  ALT=\"+4x%2A%28-x%5E4%2B10x%5E2%2B75%29%2F%28x%5E2%2B5%29%5E4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "but those numbers seem too weird for that to be the correct answer.. please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181155 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=181155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Everything is right except for one sign in the numerator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{\prime}(x)\ =\ \frac{g^{\prime}(x)h(x)\ -\ g(x)h^{\prime}(x)}{\left[h(x)\right]^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ g(x)\ =\ 2x^2\ -\ 10\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ g^{\prime}(x)\ =\ 4x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(x)\ =\ \left(x^2\ +\ 5\right)^2\">\r<BR>\n" );
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document.write( "We need the chain rule for this one:\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\">, so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{du}{dx}\ =\ 2x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{dh}{du}\ =\ 2u\ =\ 2x^2\ + 10\">, hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h^{\prime}(x)\ =\ 4x^3\ +\ 20x\">\r<BR>\n" );
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document.write( "Putting it all together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{\prime}\ =\ \frac{4x\left(x^2\ -\ 5\right)^2\ -\ \left(2x^2\ -\ 10\right)\left(4x^3\ +\ 20x\right)}{\left[x^2\ +\ 5\right]^4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{\prime}\ =\ \frac{4x\left(x^4\ -\ 10x^2\ +\ 25\right)\ -\ \left(8x^5\ +\ 40x^3\ -\ 40x^3\ -\ 200x\right)}{\left[x^2\ +\ 5\right]^4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{\prime}\ =\ \frac{4x^5\ -\ 40x^3\ +\ 100x\ -\ 8x^5\ +\ 200x}{\left[x^2\ +\ 5\right]^4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{\prime}\ =\ \frac{-4x^5\ -\ 40x^3\ +\ 300x}{\left[x^2\ +\ 5\right]^4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{\prime}\ =\ \frac{4x\left(-x^4\ -\ 10x^2\ +\ 75\right)}{\left[x^2\ +\ 5\right]^4}\">\r<BR>\n" );
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document.write( "Though I might have written it thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f^{\prime}\ =\ \frac{-4x\left(x^4\ +\ 10x^2\ -\ 75\right)}{\left[x^2\ +\ 5\right]^4}\">\r<BR>\n" );
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document.write( "But that is just changing 'happy' to 'glad' actually.\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" );
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