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Using the mean value theorem to prove the chain rule

  1. Feb 4, 2016 #1

    B3NR4Y

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    Gold Member

    1. The problem statement, all variables and given/known data
    I and J are open subsets of the real line. The function f takes I to J, and the function g take J to R. The functions are in C1. Use the mean value theorem to prove the chain rule.

    2. Relevant equations
    (g o f)' (x) = g'(f (x)) f'(x)
    MVT
    3. The attempt at a solution

    I know that the open interval (an, x) is a subset of J.

    Therefore I can apply the mean value theorem, but I have no clue where to go
     
  2. jcsd
  3. Feb 4, 2016 #2

    Svein

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    Science Advisor

    This is slightly misleading. I prefer [itex]\frac{dg}{dx}=\frac{dg}{df}\cdot \frac{df}{dx} [/itex]. That should give you a clue.
     
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