I know this is a stupid question, but it has been a long time since I did analysis. Could somebody show me how to show rigorously that $f(x)= |x|_\mathrm{eucl}^2$ is differentiable for all $x\in R^n$? I remember that the definition of differentiability involves if there exists a linear map $L$ s.t. ${|f(x+\epsilon)-f(x)-L(\epsilon)|\over|\epsilon|}\to0$ as $|\epsilon|\to0$ But is it necessary to find $L$ beforehand or is there some other way?
Sorry about this. Thank you in advance.