Let (a) Find fx (x, y) and fy (x, y) for (x, y) ≠ (0, 0). (You will find a c...

Let

(a) Find f_x (x, y) and fy (x, y) for (x, y) ≠ (0, 0). (You will find a computer algebra system helpful.)

(b) Either by hand (using limits) or by means of part (a), find the partial derivatives fx (0, y) and f_y (x, 0).

(c) Find the values of f_xy(0, 0) and f_yx (0, 0). Reconcile your answer with Theorem 4.3.