Definition 12.4.16 (Radial Laplacian).label Given a radial function $f(x)=\p(r)$ where $r=\sqrt{x_{1}^{2}+\cds+x_{n}^{2}}$ then
\begin{align*}\la f=\p''(r)+\frac{n-1}{r}\p'(r)\end{align*}
Proof. Apply chain rule.$\square$
Definition 12.4.16 (Radial Laplacian).label Given a radial function $f(x)=\p(r)$ where $r=\sqrt{x_{1}^{2}+\cds+x_{n}^{2}}$ then
Proof. Apply chain rule.$\square$
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