document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200907>Question 200907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find y' when<BR>\n" );
document.write( "y=ln(x+2)/(x^2+1)  this problem has the big ( around all)<BR>\n" );
document.write( "thanks for help<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 #151154 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=151154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming that the problem is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y=\frac{\ln(x+2)}{x^2+1}\"> right???\r<BR>\n" );
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document.write( "Recall that if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y=\frac{f(x)}{g(x)}\">, then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y^{\prime}=\frac{f^{\prime}(x)g(x)-f(x)g^{\prime}(x)}{(g(x))^2}\">\r<BR>\n" );
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document.write( "In your case, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y=\frac{\ln(x+2)}{x^2+1}\">, which means that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=\ln(x+2)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE g(x)=x^2+1\">\r<BR>\n" );
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document.write( "Now derive f and g to get: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{\prime}(x)=\frac{1}{x+2}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE g^{\prime}(x)=2x\">\r<BR>\n" );
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document.write( "Now plug these functions into the formula <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y^{\prime}=\frac{f^{\prime}(x)g(x)-f(x)g^{\prime}(x)}{(g(x))^2}\"> to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y^{\prime}=\frac{\left(\frac{1}{x+2}\right)(x^2+1)-\ln(x+2)(2x)}{(x^2+1)^2}\">\r<BR>\n" );
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document.write( "Now multiply every term by the inner LCD x+2 and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y^{\prime}=\frac{x^2+1-2x(x+2)\ln(x+2)}{(x+2)(x^2+1)^2}\">\r<BR>\n" );
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document.write( "you could perform more simplifications, but that would only change how the answer looks. </SPAN>\n" );
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