Problem

(8) (10 pts) Let $f$ be the function

$$f(x,y)= \begin{cases} \dfrac{xy^2+\frac{1}{2}y^3}{x^2+y^2}, & \text{if }(x,y)\ne(0,0) \\ 0, & \text{if }(x,y)=(0,0). \end{cases}$$

Evaluate $f_x(0,0)$ and $f_y(0,0)$ if they exist.