Answer
$$y'=-3^{-x}\ln3$$
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 $y'$: $$y'=(3^{-x})'=3^{-x}\ln 3(-x)'$$
$$y'=-3^{-x}\ln3$$
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: 68
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