Representation of functions as power series question

I am having a bit of difficulty with the representation of functions as power series. I thought I understand the basic concept and was able to do the first 15 or so problems in *Single Variable Calculus* by James Stewart (3rd ed). However, the following is one of my homework questions.

Let fn = ((sin nx) / n2). Show that the series Σ fn(x) converges for all values of x but the series of derivatives Σ f ‘n (x) diverges when x = 2n Π (PI), n is an integer. For what values of x does the series Σ f “n (x) converge?

I asked the only other student in the class I know and he couldn't do it either. So any help would be greatly appreciated.

Andrew