/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)