document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187766>Question 1187766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> All parts of this problem refer to the function below.<BR>\n" );
document.write( "y=(6+3x)5/x<BR>\n" );
document.write( "a) Use logarithmic differentiation to find dy/dx<BR>\n" );
document.write( "dydx= <BR>\n" );
document.write( "b) Find the slope of the tangent line at x=1.<BR>\n" );
document.write( "Slope = <BR>\n" );
document.write( "c) Find the equation of the tangent line at x=1.<BR>\n" );
document.write( "Tangent line: y= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819188 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=819188\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sunday, April 2, 2017<BR>\n" );
document.write( "7:06 PM\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \(6\,+\,3x\)^{5/x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln(y)\ =\ \ln\(\(6\,+\,3x\)^{5/x}\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln(y)\ =\ \frac{5}{x}\,\ln\(6\,+\,3x\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\cdot\frac{1}{y}\ =\ \frac{d}{dx}\,\[\frac{5}{x}\,\ln\(6\,+\,3x\)\]\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\cdot\frac{1}{y}\ =\ \(\frac{d}{dx}\,\frac{5}{x}\)\(\ln\(6\,+\,3x\)\)\ +\ \(\frac{5}{x}\)\(\frac{d}{dx}\,\ln\(6\,+\,3x\)\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\cdot\frac{1}{y}\ =\ \(-\frac{5}{x^2}\)\(\ln\(6\,+\,3x\)\)\ +\ \(\frac{5}{x}\)\(\frac{1}{6\,+\,3x}\)\,\frac{d}{dx}(6\,+\,3x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\cdot\frac{1}{y}\ =\ \(-\frac{5}{x^2}\)\(\ln\(6\,+\,3x\)\)\ +\ \(\frac{15}{x}\)\(\frac{1}{6\,+\,3x}\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \(6\,+\,3x\)^{5/x}\[\(-\frac{5}{x^2}\)\(\ln\(6\,+ \,3x\)\)\ +\ \(\frac{15}{x}\)\(\frac{1}{6\,+\,3x}\)\]\">\r<BR>\n" );
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document.write( "For part b, evaluate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y'(1)\">\r<BR>\n" );
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document.write( "For part c,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y(1)\ =\ y'(1)(x\,-\,1)\">\r<BR>\n" );
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document.write( "You can do your own arithmetic.\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" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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