Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 102: 8

$f’(2) = -\frac{1}{4} $

$f(x) = \frac{1}{x} $ $f’(2) = \lim\limits_{h \to 0} \frac {f(2+h)-f(2)}{h} $ $f’(2) = \lim\limits_{h \to 0} \frac{\frac{1}{2+h}-\frac{1}{2}}{h} $ $f’(2) = \lim\limits_{h \to 0} \frac{\frac{2}{4+2h}-\frac{2+h}{4+2h}}{h} $ $f’(2) = \lim\limits_{h \to 0} \frac {\frac {-h}{4+2h}}{h} $ $f’(2) = \lim\limits_{h \to 0} (\frac{-h}{4+2h})(\frac{1}{h})$ $f’(2) = \lim\limits_{h \to 0} \frac {-1}{4+2h} $ $f’(2) = -\frac{1}{4} $