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: 17



Work Step by Step

$$y=\ln(\theta+1)-e^{\theta}$$ Recall the following Derivative Rules: $$\frac{d}{dx}(\ln u)=\frac{1}{u}\frac{du}{dx}$$ $$\frac{d}{dx}(e^{x})=e^x$$ Therefore, we have $$y'=\Big(\ln(\theta+1)-e^{\theta}\Big)'=\frac{1}{\theta+1}(\theta+1)'-e^{\theta}$$ $$y'=\frac{1}{\theta+1}-e^\theta$$
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