x^3y-2x^2+y^4=8
take the derivative of each part, using the product rule on the first term
x^3 dy +y*3x^2dx -4xdx+4y^3 dy = 0
gather the dy and dx terms together
dy (x^3+4y^3) -dx(-3x^2y+4x) =0
dy terms on the left, dx terms on the right
dy (x^3+4y^3) =dx(-3x^2y+4x)
dy divided by dx
dy/dx (x^3+4y^3) =(-3x^2y+4x)
dy/dx =(-3x^2y+4x) / (x^3+4y^3)
