University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.8 - Derivatives of Inverse Functions and Logarithms - Exercises - Page 175: 85



Work Step by Step

$$y=3^{\log_2t}$$ We have the following theorems $$\frac{d}{dt}\log_au=\frac{1}{u\ln a}\frac{du}{dt}$$ $$\frac{d}{dt}(a^u)=a^u\ln a\frac{du}{dt}$$ So the derivative of $y$ is: $$y'=(3^{\log_2t})'=3^{\log_2t}\ln3(\log_2t)'$$ $$y'=3^{\log_2t}\ln3\times\frac{1}{t\ln2}(t)'$$ $$y'=\frac{3^{\log_2t}\ln3}{t\ln2}$$
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