use implicit differentiation to find dy/dx.

Question

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

Answer 1

x=-4y^3-2y/y^2-1

Answer 2

xy^2+4y^3=x-2y
x(2y)dy/x + y^2 + 12y^2 dy/dx = 1 - 2dy/dx
dy/x(2xy + 12y^2 + 2) = 1 - y^2

dy/dx = (1 - y^2)/(2xy + 12y^2 + 2)