Given the series $$f(x)=\sum_{n=1}^{\infty} (a_n\sin(nx)+b_n\cos(nx))$$
What will be a sufficient condition on the sequences $a_n$ and $b_n$ such that we can differentiate the series term-by-term?
My intuition for the condition is : the sum $\sum_{n=1}^{\infty}(|a_n|+|b_n|)$ is finite, but I have no idea how to derive it.