> > The starting point for the proof, as stated in the OP: > "Theorem. If the function w=f(x,y) together with the partial derivatives > f_x, f_y, f_xy and f_yx are continuous, then f_xy = f_yx." >
Mr Hetware, just in case you are interested in learning some elementary mathematics and not just a tedious troll, let me remind you, that these are NECESSARY hypotheses. The must be used in any valid proof. Merely MENTIONING them is not enough. They need to be USED.