Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises: 23

Answer

$\frac{\sin x}{x}+\cos x\ln(5x)$

Work Step by Step

$\frac{d}{dx}\sin x\ln(5x)$ $=\sin x\frac{d}{dx}\ln(5x)+\ln(5x)\frac{d}{dx}\sin x$ $=\sin x\frac{1}{5x}\frac{d}{dx}(5x)+\ln(5x)\cos x$ $=\sin x\frac{1}{5x}*5+\cos x\ln(5x)$ $=\frac{\sin x}{x}+\cos x\ln(5x)$
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