Question

Show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0) where f define as
f(x, y) = (-3xy)/(x^2 + y^2) if (x, y) ≠ 0 and
f(x, y) = 0 if (x, y) = (0, 0)