Remember, when you type a fraction on one line, and the numerator or denominator has more than one term, wrap it in parentheses.

With that said, implicit differentiation results in this:

* 2x+y+xy′−3y^(2)y′=0, from which

* y′=(2x+y)/(3y^(2)−x).

The point on the graph of x^(2)+xy−y^(3)=0 where dy/dx=0 is indeed where y=−2x (and also x≠3y^(2), be sure to check this later); this means that you're looking for a point that is

1. on the graph of x^(2)+xy−y^(3)=0 and

2. on the graph of y=−2x, and also

* not on the graph of x=3y^(2).

If you're finding points on the intersection between two curves given as graphs of equations, and one equation is already solved for one of the variables, you can substitute in, as you've done since introductory algebra.