The partial differential equation $$\frac{d^2u}{dt^2}=c^2\left(\frac{d^2u}{dx^2}+\frac{d^2u}{dy^2}+\frac{d^2u}{dz^2}\right) \tag{$*$}$$ is the three dimensional wave equation.
In the case of spherical symmetry, for example waves emanating from a point source, we can find a relatively simple form of the solution.
(a) Let $r=\sqrt{x^2+y^2+z^2}$ (so that $r$ represents the distance from a poitn $(x,y,z)$ in space to the origin). Show that $$\frac{d^2u}{dx^2}+\frac{d^2u}{dy^2}+\frac{d^2u}{dz^2}=\frac{d^2u}{dr^2}+ \frac 2r \frac{du}{dr}$$
I am uploading the question as a picture since I have no idea how to format that.
I am very confused as to how I would answer a).
For the left side, i could isolate each of $$\frac{\partial^2 u}{\partial x^2}, \frac{\partial^2 u}{\partial y^2}, \frac{\partial^2 u}{\partial z^2}$$ But how do I get $\displaystyle\frac{\partial^2 u}{\partial r^2}$? I don't see an equation $u$, so how would I differentiate it in terms of $r$?