what is x ^3+y ^3=18xy using implicit differentiation?

Question

How to find the derivative of this problem using implicit differentiation

Answer 1

/dx[ x^3 + y^3 = 18xy ]

       3x^2 + 3y^2 * dy/dx = 18 * [ x * dy/dx + y * 1]

       3x^2 + 3y^2 * dy/dx = 18x * dy/dx + 18y

              3y^2 * dy/dx - 18x * dy/dx = 18 y - 3x^2

            dy/dx * (3y^2 - 18x) = 18y - 3x^2

so then      dy/dx = (18y - 3x^2) / (3y^2 - 18x)

or, reducing by 3 on the right:

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