document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=235013>Question 235013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> DIFFERENTIATE WITH RESPECT TO X (x - 3)(x+3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173213 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=173213\">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( "Please do not type your questions in ALL CAPS.  It is the electronic communication s equivalent of shouting and is therefore both rude and annoying.\r<BR>\n" );
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document.write( "I presume you were given <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ (x\ -\ 3)(x\ +\ 3)\"> and you want to find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f'(x)\">\r<BR>\n" );
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document.write( "One way (the hard way) to do this would be to say that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)\ =\ g(x)h(x)\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE g(x)\ =\ (x\ -\ 3)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE h(x)\ =\ (x\ +\ 3)\">.\r<BR>\n" );
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document.write( "Then use the product rule:\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)\ =\ g(x)h(x)\">, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f'(x)\ =\ g'(x)h(x)\ +\ g(x)h'(x)\">.\r<BR>\n" );
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document.write( "For your function, using the sum and power rules:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ g(x)\ =\ (x\ -\ 3)\ \Rightarrow\ g'(x)\ =\ 1\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(x)\ =\ (x\ +\ 3)\ \Rightarrow\ h'(x)\ =\ 1\">\r<BR>\n" );
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document.write( "Therefore\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f'(x)\ = 1\,\cdot\,(x\ +\ 3)\ +\ (x\ -\ 3)\,\cdot\,1\ =\ 2x\">\r<BR>\n" );
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document.write( "The easy way is to just multiply <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)\ =\ (x\ -\ 3)(x\ + 3)\ = x^2\ -\ 9\">\r<BR>\n" );
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document.write( "Then apply the sum rule and the power rule to say <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f'(x)\ = 2x\">\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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