document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765977>Question 765977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with this problem?\r<BR>\n" );
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document.write( "Solve by means of implicit differentiation:<BR>\n" );
document.write( "(e^x) + (e^y) = (e^(x+y)).\r<BR>\n" );
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document.write( "Thanks tutors. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466566 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=466566\">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( "Just another application of the sum rule and 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(e^x\ +\ e^y\ =\ e^{x\,+\,y}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ e^x\ +\ e^y\,\cdot\,\frac{dy}{dx}\ =\ e^{x\,+\,y}\,\cdot\,\frac{d\left(x\,+\,y\right)}{dx}\">\r<BR>\n" );
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document.write( "Then second application of the sum and chain rules:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ e^x\ +\ e^y\,\cdot\,\frac{dy}{dx}\ =\ e^{x\,+\,y}\,\cdot\,\left(1\ +\ \frac{dy}{dx}\right)\">\r<BR>\n" );
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document.write( "And the rest is just a little algebra:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ e^y\,\cdot\,\frac{dy}{dx}\ -\ e^{x\,+\,y}\,\cdot\,\frac{dy}{dx}\ =\ e^{x\,+\,y}\ -\ e^x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\left(e^y\ -\ e^{x\,+\,y}\right)\ =\ e^{x\,+\,y}\ -\ e^x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{e^{x\,+\,y}\ -\ e^x}{e^y\ -\ e^{x\,+\,y}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{e^x\left(e^y\ -\ 1\right)}{e^y\left(1\ -\ e^x\right)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{e^x\left(1\ -\ e^{-y}\right)}{1\ -\ e^x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{e^x\left(e^{-y}\ -\ 1\right)}{e^x\ -\ 1}\">\r<BR>\n" );
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document.write( "Either of the last two forms are acceptable for an answer.\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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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