My attempt:
I have proved (i), it is continuous since ##\lim_{(x,y)\rightarrow (0,0)}=f(0,0)##
I also have shown the partial derivative exists for (ii), where ##f_x=0## and ##f_y=0##
I have a problem with the directional derivative. Taking u = <a, b> , I got:
$$Du =\frac{\sqrt[3] y}{3 \sqrt[3]...