Problem $3.$

Let $z=f(x,y),$ with $x=rcos$ and $y=rsin.$ Show that

$\frac{de{l}^{2}z}{del{x}^2}+\frac{de{l}^{2}z}{del{y}^2}=\frac{de{l}^{2}z}{del{r}^2}+\frac{1}{r^2}\frac{de{l}^{2}z}{\text{d}\text{e}\text{l}{}^2}+\frac{1}{r}\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{r}}$