Condition to compostion of two maps is differentiable implies each map is differential?

Question

Let $f:L\rightarrow M$ and $g:M\rightarrow N$ are homeomorphic, $L,M,N$ is normed vector spaces, $g\circ f$ is Fréchet differentiable. In which condition both $f,g$ are Fréchet differentiable? Can we say more when $L,M,N$ are $\mathbf{R}^n$?