Determine (dy/dx) using implicit differentiation.

Question

cos(X^2Y^2) = x

I'm really confused what to do now..i think the next steps are:

d/dx [cos(X^2*Y^2)] = d/dx [x]
= -sin(X^2*Y^2)* ((X^2*2Y dy/dx) + (Y^2*2X)) = 1
= -2YX^2 sin(X^2*Y^2) dy/dx + -2XY^2sin(X^2*Y^2) = 1
= -2YX^2 sin(X^2*Y^2) dy/dx = 1 + -2XY^2sin(X^2*Y^2)
= dy/dx = (1 + -2XY^2sin(X^2*Y^2))/ (-2YX^2 sin(X^2*Y^2))

Can someone tell me if this is correct?