Differentiate the equation y+ xy = 2x+y^2 and find dy/dx

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have y + xy = 2x + y^2. We have to find dy/dx

Using implicit differentiation.

dy/dx + x*dy/dx + y = 2 + 2y*dy/dx

=> dy/dx( 1 + x - 2y) = 2 - y

=> dy/dx = (2 - y) / (1 + x - 2y)

The required value of dy/dx for the given expression is dy/dx = (2 - y) / (1 + x - 2y)

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equation:

y + xy = 2x + y^2

We will use implicit differentiation to find dy/dx

We will differentiate with respect to x.

==> y' + ( x'*y + x*y') = 2 + 2yy'

==> y' + y + xy' = 2+ 2yy'

Now we will group all terms with y' on one side.

==> y' + xy' -2yy' = 2 -y

Now we will factor y'.

==> y'(1 + x -2y) = (2-y)

Now we will divide by (1+x-2y)

==> y' = (2-y)/(1+x-2y)

Then the values of dy/dx = (2-y)/(1+x-2y)

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