How can the chain rule prove the derivative of an inverse function?

[jerometurner]

Homework Statement

Assume f ^-1 (inverse) has a derivative. Use the chain rule to prove that
(f^-1)' (f(x)) = 1/f'(x)

Homework Equations

No real equations other than definition of chain rule.

The Attempt at a Solution

I'm not sure how to start other than with the definition of (f^-1) (f(x)) = x

 

[owlpride]

You have two ways of computing ((f^-1)' (f(x)))'. You could differentiate the composite function using the chain rule, or differentiate x = (f^-1)' (f(x)) directly. How do the answers compare?

 

[jerometurner]

Thanks for your help, I used the chainrule and figured it out.