Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - Chapter Review Exercises - Page 162: 11



Work Step by Step

$\frac{dy}{dx}=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$ $=\lim\limits_{h \to 0}\frac{\frac{1}{2-(x+h)}-\frac{1}{2-x}}{h}$ $=\lim\limits_{h \to 0}=\frac{\frac{(2-x)-[2-(x+h)]}{[2-(x+h)](2-x)}}{h}$ $=\lim\limits_{h \to 0}\frac{h}{[2-(x+h)](2-x)h}$ $\lim\limits_{h \to 0}\frac{1}{[2-(x+h)](2-x)}$ $=\lim\limits_{h \to 0}\frac{1}{(2-x)(2-x)}$ $=\frac{1}{(2-x)^{2}}$
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