A magnitude is a function of the position on the plane, if it is known that in polar coordinates $r$ and $\theta$ the function verifies the equation on partial derivatives $$sin(\theta) \frac{\delta F}{\delta r}+\frac {cos(\theta)}{r} \frac {\delta F}{\delta \theta}=0$$
How do I find the same equation in cartesian coordintes?
How do I transform the partial derivatives from $r$ and $\theta$ to $x$ and $y$? My guess is that I could serve from $x=rcos(\theta)$ and $y=rsin(\theta)$ but I am not sure how to handle the partil derivatives