# Let $g:= f(x,y) ||(x,y)||^4$. Prove that $g$ is differentiable on $(0,0)$

I'm having problems with the following demonstration: let $f:\mathbb{R}^2\rightarrow\mathbb{R}$ a continuous function on $(0,0)$ and let $g:= f(x,y) ||(x,y)||^4$. Prove that $g$ is differentiable on $(0,0)$.

We know by definition that the function $g$ will be differentiable on $(0,0)$ if and only if: