Derivation in Evans not reproducible

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I am currently reading in Evans where he discusses the Euler-Poisson equation on page 81.

There we have that $\displaystyle \partial_rU(x;r,t)=\frac{r}{n\alpha(n)r^n}\int_{B(x,r)}\Delta u(y,t)\mathrm{d}y$

Now he makes another derivative which is not reproducible for me

$\displaystyle \partial_{rr}U(x;r,t)=\frac{1}{\alpha(n)r^{n-1}n}\int_{\partial B(x,r)}\Delta u\mathrm{d}S+\left ( \frac{1}{n}-1\right ) \frac{1}{\alpha(n)r^n}\int_{B(x,r)}\Delta u \mathrm{d}y$

where $\alpha(n)$ is the volume of the n-th unit sphere. How is this derivative obtained?