Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 146: 76


$$\frac{d^3}{dx^3}\sin 2x = -8\cos 2x.$$

Work Step by Step

Recall that $(\sin x)'=\cos x$. Recall that $(\cos x)'=-\sin x$. We have $$\frac{d}{dx} \sin 2x=2\cos 2x $$ and $$\frac{d^2}{dx^2}\sin 2x =1\frac{d}{dx} \cos 2x=-4\sin 2x.$$ Hence, $$\frac{d^3}{dx^3}\sin 2x = -4\frac{d}{dx} \sin 2x= -8\cos 2x.$$
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