Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 13 - The Trigonometric Functions - 13.2 Derivatives of Trigonometric Functions - 13.2 Exercises - Page 688: 9

Answer

$$\frac{{dy}}{{dx}} = - 12x\cos 2x - 6\sin 2x$$

Work Step by Step

$$\eqalign{ & y = - 6x\sin 2x \cr & {\text{differentiate with respect to }}x \cr & \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ { - 6x\sin 2x} \right] \cr & {\text{use the product rule}} \cr & \frac{{dy}}{{dx}} = - 6x{D_x}\left( {\sin 2x} \right) + \sin 2x{D_x}\left( { - 6x} \right) \cr & {\text{use }}{D_x}\left( {\sin ax} \right) = a\cos ax \cr & \frac{{dy}}{{dx}} = - 6x\left( {2\cos 2x} \right) + \sin 2x\left( { - 6} \right) \cr & {\text{multiply}} \cr & \frac{{dy}}{{dx}} = - 12x\cos 2x - 6\sin 2x \cr} $$
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