I am having some trouble to derivate : I know that if I consider a map between vector spaces, $f : V\to W$ then I will have for $x\in V$ :
\begin{align} Df(x) &\in L(V,W)\\ (D(Df))(x) = D^2f(x) &\in L(V,L(V,W))\\ (D(D^2f))(x) = D^3f(x)&\in L(V,L(V,L(V,W))) \end{align} and so on...
But then I don't really understand how do derivate compositions. For example if I have $g,h : Z\to V$ and and we consider $y(t)=D^2f(g(t))(h(t))$ then how do we derive $Dy(t)$, where $t\in Z$?