Calc, derivatives?

Question

Find dx/dy for:
x^2y^3 + y^2x = 4xy - 3x

Work is appreciated, but not needed. Mostly just looking to check answer.

Answer 1

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

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

Take derivative both sides with respect to x.

x(d/dx)(y^3)+y^3(d/dx)(x) +(d/dx)(y^2) = 4(d/dx)(y) - 0

(3xy^2)(dy/dx)+y^3+2y(dy/dx)=4(dy/dx)

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

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

          =(-3x/y)+(-2/y^2)+(4/y^3)