Show that the derivative of Gateaux exists, and is the linear map, if $f$ is differentiable with the ordinary meaning.If $f:R^n \to R$ with $$f(x)={g(x)\over h(x)}$$ where $g,h \in C^{\infty}(R^n)$,with $g(0)=h(0)=0$ but $h(x) \neq 0$ when $x \in U/\{0\}$ for some open area $U$ of $0$,Find a necessary and sufficient condition for being the $f$ Gateaux differentiable at $0$, and that, consequently,the derivative of Gateaux is not necessarily linear map.
Could anyone help me(hints and ideas) how to find this condition the second part of this problem?