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

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

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

Hessian of a vector is defined by:

Any help would be sincerely appreciated.