$1\mathrm{.}2(20$ points$)$ Changing variables

There is a function $f(x,y).$ In plane polar coordinates, $x=rcos$ and $y=rsin.$ Show that

$(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}{)}^2+(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}{)}^2=(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{r}}{)}^2+\frac{1}{r^2}(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}}{)}^2$