Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.6 The Chain Rule - Exercises Set 2.6: 33

Answer

$$\frac{dy}{dx}=-6\cos^2(\sin2x)\sin(\sin2x)\cos2x$$

Work Step by Step

$$\frac{dy}{dx}=(\cos^3(\sin2x))'=3\cos^2(\sin2x)\cdot(\cos(\sin2x))'= 3\cos^2(\sin2x)(-\sin(\sin2x)\cos(\sin2x)'=-3\cos^2(\sin2x)\sin(\sin2x)\cos2x(2x)'= -3\cos^2(\sin2x)\sin(\sin2x)\cos2x\cdot2=-6\cos^2(\sin2x)\sin(\sin2x)\cos2x$$
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