document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204134>Question 1204134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If y=x²+y²=2y, find dy/dx in terms of x and y. Prove that d²y/dx²=1/(1-y)³ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840199 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Through a bit of trial-and-error, it appears the given equation should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2+=+2y ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2+=+2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Please be more careful when entering the equation.\r<BR>\n" );
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document.write( "The 1st derivative would be: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+x%2F%281-y%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+x%2F%281-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The scratch work is shown in the next section.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2y%2Aexpr%28%28dy%29%2F%28dx%29%29+=+2%2Aexpr%28%28dy%29%2F%28dx%29%29 ALIGN=MIDDLE  ALT=\"2x+%2B+2y%2Aexpr%28%28dy%29%2F%28dx%29%29+=+2%2Aexpr%28%28dy%29%2F%28dx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This will be used later.\r<BR>\n" );
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document.write( "We then apply another round of implicit differentiation with respect to x.\r<BR>\n" );
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document.write( "From here we plug in the first derivative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%5E2y%29%2F%28dx%5E2%29+=+%28%281-2y%2By%5E2%29%2Bx%5E2%29%2F%28+%281-y%29%5E3+%29 ALIGN=MIDDLE  ALT=\"%28d%5E2y%29%2F%28dx%5E2%29+=+%28%281-2y%2By%5E2%29%2Bx%5E2%29%2F%28+%281-y%29%5E3+%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=%28d%5E2y%29%2F%28dx%5E2%29+=+%281-2y%2B%28x%5E2%2By%5E2%29%29%2F%28+%281-y%29%5E3+%29 ALIGN=MIDDLE  ALT=\"%28d%5E2y%29%2F%28dx%5E2%29+=+%281-2y%2B%28x%5E2%2By%5E2%29%29%2F%28+%281-y%29%5E3+%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=%28d%5E2y%29%2F%28dx%5E2%29+=+%281-2y%2Bhighlight%28x%5E2%2By%5E2%29%29%2F%28+%281-y%29%5E3+%29 ALIGN=MIDDLE   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%5E2y%29%2F%28dx%5E2%29+=+%281-2y%2Bhighlight%282y%29%29%2F%28+%281-y%29%5E3+%29 ALIGN=MIDDLE  ALT=\"%28d%5E2y%29%2F%28dx%5E2%29+=+%281-2y%2Bhighlight%282y%29%29%2F%28+%281-y%29%5E3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the equation x^2+y^2 = 2y\r<BR>\n" );
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document.write( "Here's another way to do it \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%28%28d%5E2y%29%2F%28dx%5E2%29%29%2A%281-y%29+%2B+expr%28%28dy%29%2F%28dx%29%29%2Aexpr%28d%2F%28dx%29%29%281-y%29+=+expr%28d%2F%28dx%29%29%28x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Product Rule\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=expr%28%28d%5E2y%29%2F%28dx%5E2%29%29%2A%281-y%29+-+%28x%2F%281-y%29%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"expr%28%28d%5E2y%29%2F%28dx%5E2%29%29%2A%281-y%29+-+%28x%2F%281-y%29%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in dy/dx = x/(1-y)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%5E2y%29%2F%28dx%5E2%29+=+%28%281-2y%2By%5E2%29%2Bx%5E2%29%2F%28%281-y%29%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28d%5E2y%29%2F%28dx%5E2%29+=+%28%281-2y%2By%5E2%29%2Bx%5E2%29%2F%28%281-y%29%5E3%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=%28d%5E2y%29%2F%28dx%5E2%29+=+%281-2y%2B2y%29%2F%28%281-y%29%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28d%5E2y%29%2F%28dx%5E2%29+=+%281-2y%2B2y%29%2F%28%281-y%29%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace x^2+y^2 with 2y\r<BR>\n" );
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