I have to use Parseval's theorem for calculating: $$\sum_{n=1}^{\infty}\dfrac{1}{(a^2+n^2)^2}$$
After using the function $e^{ax}$ in period $(o,2\pi)$ I ended up with: $$\sum_{n=1}^{\infty}\frac{1}{a^2+n^2}=\frac{a\pi(e^{2a\pi}+1)}{2a^2(e^{2a\pi}-1)}-\frac{1}{2a^2}$$
The only way to come to first equation is to differentiate the second one, so when I take derivative it means necessary to take on both sides of second equation?