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: 83



Work Step by Step

$$y=\log_5e^x$$ Recall Theorem 7: $$\frac{d}{dx}\log_au=\frac{1}{u\ln a}\frac{du}{dx}$$ So the derivative of $y$ is: $$y'=\frac{1}{e^x\ln5}(e^x)'=\frac{e^x}{e^x\ln5}$$ $$y'=\frac{1}{\ln5}$$
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