Differentiate both sides of the equation with respect to x. By doing this, a dy/dx should "appear" from the y variable in the equation. Isolating the dy/dx would give you the derivative implicitly.
Differentiating both sides with respect to x:
D_x[-x^(2)y^(2)-3y^(3)+2]=D_x[5x^(3)]
This will give you:
[(-2x)(y^(2))+(2y*dy/dx)(-x^(2))]-9y^(2)*dy/dx+0=15x^(2)
-2xy^(2)-2yx^(2)*dy/dx-9y^(2)*dy/dx=15x^(2)
Put all terms with dy/dx to the left and shove the other terms to the right.
-2yx^(2)*dy/dx-9y^(2)*dy/dx=15x^(2)+2xy^(2)
Factor dy/dx out.
dy/dx*(-2yx^(2)-9y^(2))= 15x^(2)+2xy^(2)
Divide everything by (-2yx^(2)-9y^(2)). You will get the derivative.
dy/dx = (15x^(2)+2xy^(2))/(-2yx^(2)-9y^(2))
