implicit differentiate this equation in terms of y
x^2y^2=(y+1)^2(4-y^2)
It is not clear if they want the differentiation (of both sides) to be with respect to y (i.e., dx/dy) or if they want dy/dx in terms of y only.
If you do the latter, the derivative dy/dx will be a function of both x and y
Is the (4-y^2) term part of the exponent?