# Using the mean value theorem to prove the chain rule

1. Feb 4, 2016

### B3NR4Y

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. Feb 4, 2016

### Svein

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