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: 68



Work Step by Step

$$y=3^{-x}$$ Recall Theorem 5: $$\frac{d}{dx}a^u=a^u\ln a\frac{du}{dx}$$ Apply here to find $y'$: $$y'=(3^{-x})'=3^{-x}\ln 3(-x)'$$ $$y'=-3^{-x}\ln3$$
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