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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)
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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