Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 51


$$ \frac{d}{d t} \log _{3}(\sin t) =\frac{1}{\ln 3 } \cot t. $$

Work Step by Step

Recall that $(\log_b x)'=\dfrac{1}{(\ln b)x}$ Recall that $(\sin x)'=\cos x$. Thus we have: $$ \frac{d}{d t} \log _{3}(\sin t)=\frac{\cos t}{ (\ln 3) \sin t }=\frac{1}{\ln 3 } \cot t. $$ Since $\cot t=\dfrac{\cos t}{\sin t}$.
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