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Chain Rule of a functional to an exponential

  1. Apr 9, 2014 #1
    1. The problem statement, all variables and given/known data
    Suppose f is differentiable on [itex] \mathbb R[/itex] and [itex]\alpha[/itex] is a real number. Let [itex] G(x) = [f(x)]^a[/itex]

    Find the expression for [itex] G'(x)[/itex]


    2. Relevant equations

    I'm pretty sure that I got this one right, but I really want to double check and make sure.

    3. The attempt at a solution

    [itex] G'(x) = a[f(x)]^{a-1} \cdot f'(x)[/itex]
     
  2. jcsd
  3. Apr 9, 2014 #2
    Functional to an exponential.. haha. Not exactly what I meant, but okay.
     
  4. Apr 9, 2014 #3

    PeroK

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    That's correct. If you are being precise α ≠ 0.
     
  5. Apr 9, 2014 #4
    Much appreciated!
     
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