document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034951>Question 1034951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem:<BR>\n" );
document.write( "Differentiate: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+xe%5E%28x%5E2%29-arcsin%28cosx%29 ALIGN=MIDDLE  ALT=\"y+=+xe%5E%28x%5E2%29-arcsin%28cosx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649645 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=649645\">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( "You need the Sum Rule:\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(x)\ =\ u(x)\ +\ v(x)\">\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{du}{dx}\ +\ \frac{dv}{dx}\">\r<BR>\n" );
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document.write( "The Product Rule:\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(x)\ =\ u(x)\cdot v(x)\">\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ v\frac{du}{dx}\ +\ u\frac{dv}{dx}\">\r<BR>\n" );
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document.write( "And the Chain Rule:\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ u(x)\">\r<BR>\n" );
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document.write( "Then <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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}\left\[xe^{x^2}\ -\ \arcsin\left(\cos(x)\right)\right\]\">\r<BR>\n" );
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document.write( "So by the Sum Rule\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}\left\[xe^{x^2}\right\]\ -\ \frac{d}{dx}\left\[\arcsin\left(cos(x)\right)\right\]\">\r<BR>\n" );
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document.write( "For the first term, you need the Product Rule, and for the second term, the Chain Rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}\left\[x\right\]\,\cdot\,e^{x^2}\ +\ x\,\cdot\,\frac{d}{dx}\left\[e^{x^2}\right\]\ -\ \frac{1}{\sqrt{1\,-\,\cos^2x}}\,\cdot\,\frac{d}{dx}\left\[\cos(x)\right\]\">\r<BR>\n" );
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document.write( "The second term requires another application of the Chain Rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ e^{x^2}\ +\ x\,\cdot\,e^{x^2}\,\cdot\,\frac{d}{dx}\left\[x^2\right\]\ -\ \frac{-\sin(x)}{\sqrt{1\,-\,\cos^2x}}\">\r<BR>\n" );
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document.write( "Finally,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ e^{x^2}\ +\ 2x^2e^{x^2}\ +\ \frac{\sin(x)}{\sqrt{1\,-\,\cos^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" );
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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