Function that is differentiable being restricted to any linear hyperplane

Question

Need to prove that there is such a function $f : \mathbb{R}^d\rightarrow\mathbb{R}$ that
$f$ is not differentiable in $0$
But being restricted to any proper linear hyperplane $L$ $f\vert_{L}$ is differentiable in $0$
I proved it for the particular case $d = 2$. In that case $f(x;y) = {{x^3 - 3xy^2}\over{x^2+y^2}}$ is an example of such function.
Thanks.