use implicit differentiation to find dy/dx if x^3+y^3=6xy

Answer 1

3x^2 + 3y^2 dy/dx = 6x dy/dx + 6y
dy/dx(3y^2 - 6x) = 6y - 3x^2

dy/dx = (6y - 3x^2)/(3y^2 - 6x)
= (2y - x^2)/(y^2 - 2x)