Let f: $\displaystyle R^2 \rightarrow R$ be given by

f(x,y) :=

$\displaystyle \frac{xy^2}{x^2+y^4}$ if (x,y) $\displaystyle \neq$ (0,0)

0 otherwise

(a) Show that $\displaystyle d_u f(0,0)$ exists for all the vectors $\displaystyle u \in R^2$ and that $\displaystyle d_u f(0,0)$ = $\displaystyle \frac{b^2}{a}$ if u = (a,b) with a $\displaystyle \neq$ 0.

(b) Show that f is not differentiable at (0,0)

We just started this topic and I am completely lost... please help