Quote by lavinia
Right.
given a small change in x, dx, the change is x^2 is close to 2xdx and the change in y^2 is close to 2ydy. But dy = (dy/dx)dx.
If y were independent of x then dy/dx would be zero. This would just mean that x can change without a change in y. But the constraint C = x^2 + y^2 tells you that y is a function of x, at least locally.

If I were to graph all three of those "derivatives" what would they look like? How do yuo even graph F
_{x} alone?