partial differentiation with implicit function

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Suppose that $w=\frac{1}{r}f(t-\frac{r}{a})$ and that $r=\sqrt{x^2+y^2+z^2}$

Show that

$\frac{\partial^2w}{\partial x^2}+\frac{\partial^2w}{\partial y^2}+\frac{\partial^2w}{\partial z^2}=\frac{1}{a^2}\frac{\partial^2w}{\partial t^2}$

I tried to compute $\frac{\partial w}{\partial x}$, but then i don't know how to compute $\frac{\partial f}{\partial x}$.

Any hints?