Suppose that $g(z)=f(x)$, where $x=Sz+s$ for some $S\in R^{n\times n}$ and $s\in R^n$

Please Show that $\nabla g(z)=S^T\nabla f(x)$ and $\nabla^2g(z)=S^T\nabla^2 f(x) S$

where $\nabla$shows the gradient and $\nabla^2$ shows the Hessian.

Hessian of a vector is defined by:

Any help would be sincerely appreciated.