題組內容

7 Define the function \( f:\mathbb{R}^2\to \mathbb{R} \) by $$f(x, y) = \begin{cases} \frac{x\sqrt{x^2+y^2}}{|y|} & \text{if } y \neq 0 \\ 0 & \text{if } y = 0 \end{cases}$$

b. (10) Prove that the function \( f \) has directional derivatives in all directions at the point \( (0, 0) \).