Chapter 3: Derivatives - Section 3.2 - The Derivative as a Function - Exercises 3.2 - Page 115: 20

$\dfrac{1}{3}$

Use derivative formula; $f(x)= x^n \implies f'(x)= n x^{n-1}$ Consider $f(x) = 1 - \dfrac{1}{x}1-x^{-1}$ Now, $f'(x) = 0- (-1)x^{(-1-1)}=f'(x) = x^{-2}= \dfrac{1}{x^2}$ Then , we have $f'(\sqrt 3) = \dfrac{1}{(\sqrt 3)^{2}} = \dfrac{1}{3}$