document.write( "Question 990509: Find the gradient of the curve x^3+4xy-y^2=15 at the point (2,1) \n" ); document.write( "

Algebra.Com's Answer #610515 by Fombitz(32388) $\"\"$ $\"About$

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Use implicit differentiation,
\n" ); document.write( " $\"3x%5E2dx%2B4%28xdy%2Bydx%29-2ydy=0\"$
\n" ); document.write( " $\"3x%5E2dx%2B4xdy%2B4ydx-2ydy=0\"$
\n" ); document.write( " $\"%284x-2y%29dy=-%283x%5E2%2B4y%29dx\"$
\n" ); document.write( " $\"dy%2Fdx=-%28%283x%5E2%2B4y%29%2F%284x-2y%29%29\"$
\n" ); document.write( "So when $\"x=2\"$ and $\"y=1\"$ ,
\n" ); document.write( " $\"dy%2Fdx=-%28%283%282%29%5E2%2B4%281%29%29%2F%284%282%29-2%281%29%29%29\"$
\n" ); document.write( " $\"dy%2Fdx=-%28%2812%2B4%29%2F%288-2%29%29\"$
\n" ); document.write( " $\"dy%2Fdx=-%2816%2F6%29\"$
\n" ); document.write( " $\"dy%2Fdx=-%288%2F3%29\"$
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