document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187769>Question 1187769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use logarithmic differentiation to find the derivative of the function.<BR>\n" );
document.write( "y=(ln(x+8))^x\r<BR>\n" );
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document.write( "y′= <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819153 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819153\">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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \ln^x(x\,+\,8)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln y\ =\ \ln(\ln^x(x\,+\,8)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\,\frac{1}{y}\ =\ \frac{d}{dx}x\,\cdot\,\(\ln\(\ln\(x\,+\,8\)\)\)\ +\ x\,\cdot\,\frac{d}{dx}\ln\(\ln\(x\,+\,8\)\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\,\frac{1}{y}\ =\ \(\ln\(\ln\(x\,+\,8\)\)\)\ +\ \frac{x}{\ln(x\,+\,8)}\,\cdot\,\frac{d}{dx}\ln\(x\,+\,8\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\,\frac{1}{y}\ =\ \(\ln\(\ln\(x\,+\,8\)\)\)\ +\ \frac{x}{\ln(x\,+\,8)}\,\cdot\,\frac{1}{(x\,+\,8)}\,\cdot\,\frac{d}{dx}\(x\,+\,8\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\,\frac{1}{y}\ =\ \(\ln\(\ln\(x\,+\,8\)\)\)\ +\ \frac{x}{\ln(x\,+\,8)}\,\cdot\,\frac{1}{(x\,+\,8)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ y\,\cdot\,\(\ln\(\ln\(x\,+\,8\)\)\)\ +\ \frac{x}{\ln(x\,+\,8)}\,\cdot\,\frac{1}{(x\,+\,8)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \ln^x(x\,+\,8)\,\cdot\,\[\(\ln\(\ln\(x\,+\,8\)\)\)\ +\ \frac{x}{\ln(x\,+\,8)}\,\cdot\,\frac{1}{(x\,+\,8)}\]\">\r<BR>\n" );
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document.write( "																<BR>\n" );
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( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
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