Using the mean value theorem to prove the chain rule

[B3NR4Y]

Homework Statement

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.

Homework Equations

(g o f)' (x) = g'(f (x)) f'(x)
MVT

The Attempt at a Solution

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

Therefore I can apply the mean value theorem, but I have no clue where to go

 

[Svein]

Homework Equations

(g o f)' (x) = g'(f (x)) f'(x)

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