Originally Posted by

**Stonehambey** Hi,

The proof is from Trench's Introduction to Real Analysis, which can be freely downloaded here

William Trench - Trinity University Mathematics
I was wary of posting the entire proof verbatim in case of any infringement (not sure what the laws are concerning mathematical proofs but I thought it better to be safe).

The proof in question is on page 78 of the book.

Thanks,

Stonehambey

EDIT: Actually I believe there may be a bracket missing from equation (10) in the proof, immediately after $\displaystyle f'(g(x_0))$. Can anyone confirm this?

Ha! Luckily for you I own Trench, I don't think many people would download it . Anyways the part you mention reads

$\displaystyle \displaystyle \frac{h(x)-h(x_0)}{x-x_0}=\left[f'\left(g(x_0)+E(g(x))\right]\frac{g(x)-g(x_0)}{x-x_0}\right]$

when it should read

$\displaystyle \displaystyle \frac{h(x)-h(x_0)}{x-x_0}=\left[f'\overbrace{(g(x_0))}^{\text{here}}+E(g(x))\right]\frac{g(x)-g(x_0)}{x-x_0}\right]$