
Implicit Differentiation
Find dy/dx by implicit differentiation. Well I've gotten the right answers on several of the problems, but for this problem my answer seems way off. I think it's because I'm messing up the chain rule somehow.
x^3xy+y^2 = 4
3x^2[(x)(dy/dx)+(1)(y)]+2y = 0
3x^2[(x)(dy/dx)]y+2y = 0
(x)(dy/dx) = 3x^2y
dy/dx = (3x^2y) / (x)
The answer I'm suppose to arrive at is (y3x^2) / (2yx).
My answer has a fairly similiar numerator but the denominator is way off.
Any help is appreciated. (Happy)

Problem starts here
3x^2[(x)(dy/dx)+(1)(y)]+2ydy/dx = 0