Hey guys Im not sure how to do this and would be delighted with any help. I was thinking simplifying (f ^{-1 }o f)(x) and then chain rule.
Suppose that (a, b) to(c, d) is a bijection,and that f is differentiable on (a, b). Assuming that this implies that the inverse function
f ^{-1} : (c, d) to (a, b) is differentiable on (c, d), show that if y_{0} element of(c; d) and x_{0}= f ^{-1}(y_{0}) then,
(f ^{-1})'(y_{0}) = 1/f '((f ^{-1})(y_{0})), if f '(x_{0}) is not 0