Let $E$ be a real pre-Hilbert space. Show that in $E$ the mapping $x\to\||x||$ of $E$ into $\mathbf{R}$ is differentiable at every point $x\ne0$ and that its derivative at such a point is the linear mapping $$s\to\frac{(s\mid x)}{||x||}.$$ I am not sure what this $(s\mid x)$ means. However, I t...