Basic Analysis I — Real Analysis · Problem 4.1.10

The Derivative — Jiri Lebl

Mathematics — Real Analysis · derivative-inverse-function

Problem

Let

I_1, I_2

be intervals. Let

f : I_1 \to I_2

be a bijective function and

g : I_2 \to I_1

be the inverse. Suppose that both

f

is differentiable at

c \in I_1

and

f'(c) \neq 0

and

g

is differentiable at

f(c)

. Use the chain rule to find a formula for

g'\bigl(f(c)\bigr)

(in terms of

f'(c)