My question is probably simple to many of you, but I find it confusing and I am trying to improve. How do I take the Laplacian of $|x|$ where $x=(x_1, x_2, ... , x_n)$?
$\Delta |x|=$
I got used to doing these sorts of calculations in 3 dimensions, but I have since moved on to the $\mathbb{R}^n$ case and I think I need to see some examples and a step-by-step procedure. I know that we need to take the second partial derivatives and add them up, but I can't seem to wrap my mind around moving past the 3 dimensional case.
Try writing $|x| = \sqrt{x_1^2 + \cdots + x_n^2}$, and then compute the second derivatives $\partial_{x_j}^2$ for $j\in[n]$ and sum.