# Differentiation of Fourier Series

The Series: $$\frac{\pi}{2}-\frac{4}{\pi}\sum_{n=1}^{\infty}\frac{\cos(2n-1)x}{(2n-1)^2}$$ is the Fourier cosine series for the function $f(x)=x$ on the interval $0<x<\pi$. Differentiate this series term by term to obtain a representation for the derivative $f^{'}(x)=1$ on that interval. State why the procedure is reliable here.