Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 386: 22


$$ f'(\theta)= \frac{ 1}{\theta} \cos(\ln\theta).$$

Work Step by Step

Recall that $(\ln x)'=\dfrac{1}{x}$ Recall that $(\sin x)'=\cos x$. Since $ f(\theta)=\sin ( \ln\theta)$, then the derivative, using the chain rule, is given by $$ f'(\theta)=\cos( \ln \theta) (\ln \theta)'= \cos (\ln\theta )\frac{ 1}{\theta}=\frac{ 1}{\theta} \cos(\ln\theta).$$
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