Let $\displaystyle f,g:E\longrightarrow F$ (finite normed vector spaces) be differentiable functions. Use the chain rule to prove that $\displaystyle f+g$ is also differentiable.

The chain rule has to do with composite functions, I know, so I know somehow I have to think of $\displaystyle f+g$ as a composite function, but I'm just not seeing it.