Answer
$\frac{3}{2}$
Work Step by Step
Formula in Exercise 83: $(f^{-1})'(x)=\frac{1}{f'(f^{-1}(x))}$
Given: $f(4)=5$ and $f'(4)=\frac{2}{3}$.
Assuming $f$ is one-to-one, $f^{-1}(5)=4$.
Using the formula above,
$(f^{-1})'(5)=\frac{1}{f'(f^{-1}(5))}=\frac{1}{f'(4)}=\frac{1}{\frac{2}{3}}=\frac{3}{2}$
