document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374974>Question 374974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evening Everyone.<BR>\n" );
document.write( "    Been a while since i attempeted anything like this and trying to brush up a little, i have attempted to anser the first two parts if somebody would be so kind as to check them and assist on the third part\r<BR>\n" );
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document.write( "Use the chain rule to find the derivatives of the following functions:<BR>\n" );
document.write( "(a) y = e^-x2 <BR>\n" );
document.write( "I Got = -2e^(-x^2)<BR>\n" );
document.write( "(b) y = cos(3x^2 + 2x) <BR>\n" );
document.write( "I Got = (-Sin).(3x^2+2x).(6x+2)<BR>\n" );
document.write( "(c) y = sin^2(3x^2 - 1)\r<BR>\n" );
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document.write( "Thank You in antiscipation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266669 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=266669\">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( "a)\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large u\ =\ -x^2\">, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ e^u\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{du}\ =\ e^u\ =\ e^{-x^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{du}{dx}\ =\ -2x\">\r<BR>\n" );
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document.write( "Hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{dy}{du}\,\cdot\,\frac{du}{dx}\ =\ -2xe^{-x^2}\">\r<BR>\n" );
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document.write( "Part b you got spot on.\r<BR>\n" );
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document.write( "Part c just requires you to extend the chain rule, which can be done indefinately.  So, instead of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{dy}{du}\,\cdot\,\frac{du}{dx}\">\r<BR>\n" );
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document.write( "you need to use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{dy}{du}\,\cdot\,\frac{du}{dv}\,\cdot\,\frac{dv}{dx}\">\r<BR>\n" );
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document.write( "For:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \sin^2\left(3x^2\ -\ 1\right)\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE v\ =\ 3x^2\ -\ 1\">, hence <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{dv}{dx}\ =\ 6x\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE u\ =\ \sin(v)\">, hence <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{du}{dv}\ =\ \cos(v)\ =\ \cos\left(3x^2\ -\ 1\right)\">\r<BR>\n" );
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document.write( "And <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ =\ u^2\">, hence <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{dy}{du}\ =\ 2u\ =\ 2\sin(v)\ =\ 2\sin\left(3x^2\ -\ 1\right)\">\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 \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{dy}{du}\,\cdot\,\frac{du}{dv}\,\cdot\,\frac{dv}{dx}\ =\ 12x\sin\left(3x^2\ -\ 1\right)\cos\left(3x^2\ -\ 1\right)\">\r<BR>\n" );
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document.write( "By the way, the rule is one question per post.  I let you slide because you had attempted two of your three problems.\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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