Answer
$$y'=\frac{1}{\ln5}$$
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: $$y'=\frac{1}{e^x\ln5}(e^x)'=\frac{e^x}{e^x\ln5}$$
$$y'=\frac{1}{\ln5}$$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
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
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