document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133146>Question 1133146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Y=[15e^(-x)]/[x+e^(-2x)]<BR>\n" );
document.write( "Solve dy/dx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750343 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=750343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2815e%5E%28-x%29%29%2F%28x%2Be%5E%28-2x%29%29 ALIGN=MIDDLE  ALT=\"y=%2815e%5E%28-x%29%29%2F%28x%2Be%5E%28-2x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2815%281%2Fe%5Ex%29%29%2F%28x%2B1%2Fe%5E%282x%29%29 ALIGN=MIDDLE  ALT=\"y=%2815%281%2Fe%5Ex%29%29%2F%28x%2B1%2Fe%5E%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2815%2Fe%5Ex%29%2F%28%28x%2Ae%5E%282x%29%2B1%29%2Fe%5E%282x%29%29 ALIGN=MIDDLE  ALT=\"y=%2815%2Fe%5Ex%29%2F%28%28x%2Ae%5E%282x%29%2B1%29%2Fe%5E%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2815e%5E%282x%29%29%2F%28x%2Ae%5Ex%2A%28e%5E%282x%29%2B1%29%29 ALIGN=MIDDLE  ALT=\"y=%2815e%5E%282x%29%29%2F%28x%2Ae%5Ex%2A%28e%5E%282x%29%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2815e%5Ex%29%2F%28%28x%2Ae%5E%282x%29%2B1%29%29 ALIGN=MIDDLE  ALT=\"y=%2815e%5Ex%29%2F%28%28x%2Ae%5E%282x%29%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+ ALIGN=MIDDLE  ALT=\"dy%2Fdx+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%2Fdx%29%28%2815e%5Ex%29%2F%28x%2Ae%5E%282+x%29+%2B+1%29%29 ALIGN=MIDDLE  ALT=\"%28dy%2Fdx%29%28%2815e%5Ex%29%2F%28x%2Ae%5E%282+x%29+%2B+1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = > first take the constant out\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%2Fdx%29%28%2815e%5Ex%29%2F%28x%2Ae%5E%282+x%29+%2B+1%29%29=15%28dy%2Fdx%29%28%2815e%5Ex%29%2F%28x%2Ae%5E%282+x%29+%2B+1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply the Quotient Rule: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2Fg ALIGN=MIDDLE  ALT=\"f%2Fg\"   DISABLED_style= \"max-width:90%; height:auto;\" >'=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >'*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f ALIGN=MIDDLE  ALT=\"+f\"   DISABLED_style= \"max-width:90%; height:auto;\" >)/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5E2 ALIGN=MIDDLE  ALT=\"g%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%2Fdx%29%28%2815e%5Ex%29%2F%28x%2Ae%5E%282+x%29+%2B+1%29%29=15%2A%28dy%2Fdx%29%28e%5Ex%2A%28xe%5E%282x%29%2B1%29-%28d%2Fdx%29%28x%2Ae%5E%282x%29%2B1%29e%5Ex%29%2F%28x%2Ae%5E%282x%29%2B1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply the common derivative:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29e%5Ex=e%5Ex ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29e%5Ex=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%28xe%5E%282x%29%2B1%29=e%5E%282x%29%2B2e%5E%282x%29%2Ax ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%28xe%5E%282x%29%2B1%29=e%5E%282x%29%2B2e%5E%282x%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%2Fdx%29%28%2815+e%5Ex%29%2F%28x%2Ae%5E%282+x%29+%2B+1%29%29=15%28e%5Ex%2A%28x%2Ae%5E%282x%29%2B1%29%29-%28e%5E%282x%29%2B2e%5E%282x%29%2Ax%29e%5Ex%29%2F%28%28x%2Ae%5E%282x%29%2B1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2815%28e%5Ex%2A%28x%2Ae%5E%282x%29%2B1%29%29-%28%28e%5E%282x%29%2B2e%5E%282x%29%2Ax%29e%5Ex%29%29%2F%28%28x%2Ae%5E%282x%29%2B1%29%5E2%29+%29%2F%28+15%28e%5Ex-e%5E%283x%29%2Ax-e%5E%283x%29%29%2F%28e%5E%282x%29%2Ax%2B1%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%2Fdx%29%28%2815+e%5Ex%29%2F%28x+%2Ae%5E%282+x%29+%2B+1%29%29=+15%28e%5Ex%2A%28x%2Ae%5E%282x%29%2B1%29-%28e%5E%282x%29%2B2e%5E%282x%29%2Ax%29e%5Ex%29%2F%28x%2Ae%5E%282x%29%2B1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%2A%28x%2Ae%5E%282x%29%2B1%29-%28e%5E%282x%29%2B2e%5E%282x%29%2Ax%29e%5Ex%29%2F%28x%2Ae%5E%282x%29%2B1%29%5E2=%28e%5Ex-e%5E%283x%29%2Ax-e%5E%283x%29%29%2F%28e%5E%282x%29%2Ax%2B1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%2Fdx%29%28%2815+e%5Ex%29%2F%28x+e%5E%282+x%29+%2B+1%29%29=+15%28e%5Ex-e%5E%283x%29%2Ax-e%5E%283x%29%29%2F%28e%5E%282x%29%2Ax%2B1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );