document.write( "Question 1187871: Please help me with my assignment.
\n" ); document.write( "Use Implicit differentiation to find the Derivative of y with respect to x.
\n" ); document.write( "1. Find the slope of a tangent line to th graph of x^2y^2-xy+x=1 at (1,1)? \n" ); document.write( "

Algebra.Com's Answer #818903 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Please help me with my assignment.
\n" ); document.write( "Use Implicit differentiation to find the Derivative of y with respect to x.
\n" ); document.write( "1. Find the slope of a tangent line to th graph of x^2y^2-xy+x=1 at (1,1)?
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document.write( "You should differentiate this identity.\r\n" );
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document.write( "To facilitate it, differentiate each addend separately.\r\n" );
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document.write( "    (x^2*y^2)' = 2x*y^2 + 2x^2*y*y' \r\n" );
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document.write( "    (xy)' = y + xy'\r\n" );
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document.write( "    x' = 1\r\n" );
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document.write( "    1' = 0.\r\n" );
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document.write( "Then combine these derivatives in one formula\r\n" );
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document.write( "    2x*y^2 + 2x^2*y*y' - y - xy' + 1 = 0\r\n" );
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document.write( "Keep the terms with y' on the left side; move the rest of the terms to the right side\r\n" );
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document.write( "    2x^2*y*y' - xy' = 2x*y^2 + y - 1\r\n" );
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document.write( "In the left side, factor out the common factor y'\r\n" );
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document.write( "    (2x^2*y - x)*y' = 2x*y^2 + y - 1\r\n" );
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document.write( "Express y', dividing both sides by  (2x^2*y - x)\r\n" );
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document.write( "    y' = .\r\n" );
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document.write( "Thus the formula is just ready.\r\n" );
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document.write( "To get the value,  substitute the values  x= 1, y= 1 into the formula.  You will get then\r\n" );
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document.write( "    y' =  =  =  = 2.    ANSWER\r\n" );
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document.write( "ANSWER.  y' = 2.\r\n" );
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