Let $f,g:\Bbb{R}^n\to\Bbb{R} $ be defined by $f(x)=\langle x,x\rangle$ and $g(x)=\sqrt{\langle x,x\rangle}\,,$ respectively.

Prove that $f$ and $g$ are differentiable on $\Bbb{R}^n$ and $\Bbb{R}^n-\{0\}$, respectively and compute $f'(x)$ and $g'(x).$

If I may ask, does this $\langle x,x\rangle$ also mean inner product? If yes, my problem is half solved. If no, I would need some nice proofs.