Answer
$\displaystyle \frac{1}{6}$
Work Step by Step
Apply Th. 1: the derivative rule for inverses.
If $f(b)=a$, then
$\displaystyle \left.\frac{df^{-1}}{dx}\right|_{x=a}\ \ =\ \ \frac{1}{\left.\frac{df}{dx}\right|_{x=b}}$
We are given $f(5)=0,\qquad (a=0, b=5)$
$f(x)=x^{2}-4x-5$
$\displaystyle \frac{df}{dx}=2x-4$
$\displaystyle \left.\frac{df^{-1}}{dx}\right|_{x=0}\ \ =\ \ \frac{1}{\left.\frac{df}{dx}\right|_{x=5}}=\frac{1}{2(5)-4}=\frac{1}{6}$
