real analysis - Show that the function $f(x) = begin{cases} frac{x^2y^4}{x^4+y^8} ,& text{if } (x,y)≠ (0,0) \ 0, &text{if } (x,y)= (0,0)end{cases}$ is Gateaux

Show that the function

$$f(x) = \begin{cases} \frac{x^2y^4}{x^4+y^8} ,& \text{if } (x,y)≠ (0,0) \\ 0, &\text{if } (x,y)= (0,0)\end{cases}$$

is Gateaux differentiable at $(0,0)$ but not continuous at $(0,0)$.

So I know how to show it is Gateaux differentiable at $(0,0)$, but I don't know how to go about showing it is not continuous...