Code:
\[ \frac{\partial U}{\partial r}=\frac{\frac{\partial P}{\partial r}Q-P\frac{\partial Q}{\partial r}}{P^{2}+Q^{2}}\quad\frac{\partial U}{\partial\theta}=\frac{\frac{\partial P}{\partial\theta}Q-P\frac{\partial Q}{\partial\theta}}{P^{2}+Q^{2}} \]