document.write( "Question 1208278: Find dy/dx for x^3+2xy^2 = sin y \n" ); document.write( "

Algebra.Com's Answer #846598 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "Find dy/dx for x^3+2xy^2 = sin y
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document.write( "Starting equation is\r\n" );
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document.write( "    x^3 + 2xy^2 = sin(y).    (1)\r\n" );
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document.write( "Here by default we consider x as an independent variable and y as a function of x \r\n" );
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document.write( "    y = y(x).\r\n" );
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document.write( "Differentiate the given equation (1) (both sides separately).  \r\n" );
document.write( "Follow standard rules of differentiating. You will get\r\n" );
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document.write( "    3x^2 + 2y^2 + 4xy*y' = cos(y)*y'    (2)\r\n" );
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document.write( "where y' = y'(x) =  for brevity.\r\n" );
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document.write( "Collect and combine the terms in formula (2) in order for to have y' \r\n" );
document.write( "as a factor on one side of the equation\r\n" );
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document.write( "    3x^2 + 2y^2 = cos(y)*y' - 4xy*y' ,\r\n" );
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document.write( "    3x^2 + 2y^2 = (cos(y) - 4xy)*y' .\r\n" );
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document.write( "Now express y'\r\n" );
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document.write( "    y' = .    ANSWER\r\n" );
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document.write( "It is the formula which you want to get.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Having this idea, this technique and this TEMPLATE in your mind,
\n" ); document.write( "you can solve million other similar problems.\r
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