The function $f(x)=x^3+x$ is one-to-one and differentiable, with $f(1)=2$. What is $(f^{-1})'(2)$?

Core Concept

First, $f'(x)=3x^2+1$, so $f'(1)=4$. Since $f^{-1}(2)=1$, the formula gives $(f^{-1})'(2)=\frac{1}{f'(1)}=\frac{1}{4}$.