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: 9


$-2x $

Work Step by Step

$\frac{dy}{dx}=\lim\limits_{h\to 0}\frac{f(x+h)-f(x)}{h}$ $=\lim\limits_{h \to 0}\frac{[4-(x+h)^{2}]-(4-x^{2})}{h}$ $=\lim\limits_{h \to 0}\frac{x^{2}-(x+h)^{2}}{h}$ $=\lim\limits_{h \to 0}\frac{x^{2}-x^{2}-h^{2}-2xh}{h}$ $\lim\limits_{h \to 0}(-h-2x)=-2x $
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