document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93947>Question 93947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> differentiate with respect to x :  loge3x-3/x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68413 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=68413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> differentiate with respect to x : loge3x-3/x\r<BR>\n" );
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document.write( "First term:<BR>\n" );
document.write( "ln(3x)=ln3+lnx\r<BR>\n" );
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document.write( "d/dx(ln3)+d/dx(lnx)=0+1/x=1/x\r<BR>\n" );
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document.write( "Second term:\r<BR>\n" );
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document.write( "-3/x=-3x^(-1)\r<BR>\n" );
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document.write( "d/dx(-3x^(-1))=3x^(-2)\r<BR>\n" );
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document.write( "So we have:\r<BR>\n" );
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document.write( "1/x+3x^(-2) and we can simplify this:\r<BR>\n" );
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document.write( "1/x+3/x^2  multiply each term by (x^2)/(x^2):\r<BR>\n" );
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document.write( "(x+3)/x^2\r<BR>\n" );
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document.write( "Hope this helps--ptaylor<BR>\n" );
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