I would like to know how to show the following:
Let f(x)= summation of an (note that n is subscript) * (Sin nx)
so f(x) = summation (an)(Sin nx).
If the series summation of n(an) is absolutely convergent, show that f is differentiable and f'(x)= summation of n(an)(cos nx).
Can someone please help me on this? Thank you!
I would also like to know what theorem on series of derivatives should we apply.