Old arguments deleted. Look `em up in the history pages.
Discussion of Rewrite
Before we get into an edit war - if anyone really doesn't like the rewrite I would hope we could discuss it first.
The basic question that prompted this is what is the page about. Supposedly it is about inverse functions and differentiation. Not inverse functions (all my technical stuff and examples). Not differentiation. But the two concepts together, which can only mean the reciprocal relation between the derivatives.
The idea is to get to the point as fast as possible, point people who want to know more about inverse functions and calculus at the right places, and then gives some examples not just of inverse functions but of the whole reciprocal thing.
Only the one really simple proof is needed in my opinion. And lets make full use of the chain rule - people who want details can look there.
The integral formula stuff for the inverse function had errors in it. I've fixed it up so that it is now true. Functions can be differentiable but non-invertible - even locally!
Best Wishes hawthorn