Solution
= Solution
For the positive <Euclidean norm> $r=(x_1^2+x_2^2+x_3^2)^{1/2}$, the <chain rule> gives
$$
\boxed{\partial_i r=\frac12(x_jx_j)^{-1/2}(2x_i)=\frac{x_i}{r},\qquad \nabla r=\widehat{\mathbf x}.}
$$
Repeated indices use the <Einstein summation convention>. The origin is excluded because the <Euclidean norm> is not differentiable there. Another derivative, useful below, is $\partial_i\widehat x_j=\delta_{ij}/r-x_ix_j/r^3$, with $\delta_{ij}$ the <Kronecker delta>.