I've this function : $$ f(x,y)= \begin{cases} \dfrac{(1+x^2)x^2y^4}{x^4+2x^2y^4+y^8} \quad \text{ for } \qquad (x,y)\ne (0,0) \\ 0 \quad \quad \quad \quad \quad \quad \quad \quad \text{ for } \quad (x,y)=(0,0) \end{cases}$$
This function isn't continuous in $(0,0)$ so isn't differentiable in $(0,0)$. But what can i said about the existence of all the directional derivatives in $(0,0)$?