Differentiate : 2y^2 + x^3 = 2xy + 5

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to differentiate 2y^2 + x^3 = 2xy + 5

Using implicit differentiation we get

4y*(dy/dx) + 3*x^2 = 2x*(dy/dx) + 2y

=> (dy/dx) (4y - 2x) = 2y - 3*x^2

=> dy/dx = (2y - 3*x^2)/(4y - 2x)

The required derivative dy/dx = (2y - 3*x^2)/(4y - 2x)

 

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

Posted on

Given the equation:

2y^2 + x^3 = 2xy + 5

We need to find the derivative y'

We will use implicit differentiation.

==> 4y*y' + 3x^2 = (2x)'*y + (2x)*y' + 0

==> 4yy' + 3x^2 = 2y + 2xy'

Now we will combine terms with y'.

==> 4yy' - 2xy' = 2y - 3x^2

Now we will factor y'.

==> y'( 4y - 2x) = 2y-3x^2

Now we will divide by (4y-2x)

==> y' = (2y-3x^2)/(4y-2x)

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