Let $\displaystyle F: R^n \rightarrow R^m$ and $\displaystyle G: R^m \rightarrow R^p$ be mappings. Prove that their composition $\displaystyle GF: R^n \rightarrow R^p$ is a differentiable mapping. (Take $\displaystyle m=p=2$ for simplicity). Then show that $\displaystyle (GF)_* = G_*F_*$.

I do not know how to prove this and would appreciate some help. Thanks!