The equation 4x^2y - 3y = x^3 implicitly defines y as a function of x.

a) use implicit differentiation to find dy/dx.

b) write y as an explicit function of x and compute dy/dx directly. Show that the results of parts a and b are equivalent.

I don't know how to show that they are equivalent :( please help thanks..

4x^2y - 3y = x^3

The above is unclear; is (2y) the exponent? I am guessing only the 2 is an exponent.



I'll do Part b):

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

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

y' = [ (4x^2 - 3)(3x^2) - (x^3)(8x) ] / (4x^2 - 3)^2