I encountered the following passage in a paper, in witch $K$ is a general function of $\theta$ and $\phi$ expanded in Fourier series:
$K=\sum_{lm} K_{lm}\exp[i(l\theta-m\phi)]$ $\implies \frac{\partial K}{\partial \theta}=\mathrm{Re}\sum_{lm} ilK_{lm}\exp[i(l\theta-m\phi)]$
I don't understand why the real part is taken. Is seems like it is a consequence of the differentiation, but I can't see why.