I just had my first lecture of my analysis course, and we were introduced the differentiation on general euclidean space where the derivative is regarded as a linear transformation.
Define $f\colon\mathbb R^n\to\mathbb R$ by $f(x)=|x|$ (the norm of x). Determine the set of points at which f is differentiable and find the derivative there.
I am crazy comparing this to the absolute value function ($f\colon \mathbb R\to\mathbb R$ defined by $f(x)=|x|$), yet quite confused about how to write proofs using the definition of the linear-transformation form derivatives.
I think the answer should be $f(x)$ is anywhere differentiable except $0$ in $\mathbb R^n$, however I cannot write down the proof. I wish I can get some help here.