Question 2
Let $f(x, y) = \begin{cases} \frac{xy(x^2 - y^2)}{x^2 + y^2}, & \text{if } (x, y) \neq (0, 0) \\ 0, & \text{if } (x, y) = (0, 0) \end{cases}$
(1) Compute $f_x$ and $f_y$ for $(x, y) \neq (0, 0)$.
(2) Use the definition of partial derivatives, compute $f_x(0, 0)$ and $f_y(0, 0)$.
(3) Does $f$ have continuous partial derivatives?