For the function $f(x, y) = \begin{cases} xy\frac{x^2 - y^2}{x^2 + y^2}, & \text{if } (x, y) \neq (0, 0) \\ 0, & \text{if } (x, y) = (0, 0) \end{cases}$ \\
i. Show that $f_x(x, 0) = x$ and $f_y(0, y) = -y$. \\
ii. Show that $f_{xy}(0, 0) \neq f_{yx}(0, 0)$.