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

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)