Let (x, y) = (xy) 1/3 . (a) Use the limit definition to show that x(0, 0) = y(0, 0) = 0. (b) Use the

Let ƒ(x, y) = (xy)^1/3.

(a) Use the limit definition to show that ƒx(0, 0) = ƒy(0, 0) = 0.
(b) Use the limit definition to show that the directional derivative Du ƒ(0, 0) does not exist for any unit vector u other than i and j.
(c) Is f differentiable at (0, 0)?