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Is showing that a series of functions is differentiable as simple as it appears?

  1. Jan 22, 2012 #1
    Here is the problem and my want. I think I might be overlooking something because it seems rather simple...


  2. jcsd
  3. Jan 22, 2012 #2


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    "Hence"? how do you know you can differentiate this infinite sum of differentiable functions? what rule tells you that? do you know the weierstrass "M test"?
  4. Jan 22, 2012 #3
    Yes, I have access to the Weierstrass M-test. But that seems to deal with uniform convergence, and it doesn't quite seem to deal with differentiability or continuity. Unless I'm misunderstanding it.
  5. Jan 22, 2012 #4
    Straight from a book:

    "If, on differentiating a convergent infinite series [itex] \sum_{v = 0}^{\infty} G_v(x) = F(x) [/itex] term by term, we obtain a uniformly convergent series of continuous terms [itex] \sum_{v = 0}^{\infty} g_v(x) = f(x) [/itex], then the sum of this last series is equal to the derivative of the sum of the first series"
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