# Series of functions and differentiating term by term

1. Nov 18, 2013

### mahler1

I have to solve a bunch of exercises related to function series and in some of them they ask me whether a particular series converges uniformly if one differentiates it term by term. So here I came up with a doubt: When $\sum_0^{\infty} f_n(x)$ can be differentiated term by term? What hypothesis do I need to do that? Does the series have to converge to a differentiable function or I can differentiate each term without even asking the series to be convergent? I am very confused with this.

2. Nov 18, 2013

### iRaid

3. Nov 19, 2013

### mahler1

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