題組內容

2. Consider $$ f(x, y) = \begin{cases} \dfrac{x y^2}{x^2 + y^2}, & \text{if } (x, y) \neq (0, 0); \\ 0, & \text{if } (x, y) = (0, 0). \end{cases} $$

(b) (6 points) Use the definition of the directional derivative to find $ D_u(0, 0) $ for all unit vectors $ \mathbf{u} = (a, b) $.