A one-to-one differentiable function $f$ satisfies $f(2)=5$ and $f'(2)=3$. What is $(f^{-1})'(5)$?

Core Concept

Since $f(2)=5$, the inverse satisfies $f^{-1}(5)=2$. The formula gives $(f^{-1})'(5)=\frac{1}{f'(2)}=\frac{1}{3}$.