University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.2 - The Derivative as a Function - Exercises: 23

Answer

$f'(x) = \frac{-1}{(x+2)^{2}}$

Work Step by Step

$f(x) = \frac{1}{x+2}$ $f'(x) = \lim\limits_{z \to x}\frac{\frac{1}{z+2} - \frac{1}{x+2}}{z-x}$ $f'(x) =\lim\limits_{z \to x}\frac{1}{z-x}\frac{x-z}{(z+2)(x+2)}$ $f'(x) =\lim\limits_{z \to x}\frac{-1}{(z+2)(x+2)}$ $f'(x) = \frac{-1}{(x+2)^{2}}$
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