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: 72



Work Step by Step

$$y=t^{1-e}$$ Recall the General Power Rule for Derivatives: $$\frac{d}{dt}t^n=nt^{n-1}$$ Apply here to find $y'$: $$y'=(t^{1-e})'=(1-e)t^{(1-e)-1}=(1-e)t^{-e}$$ $$y'=\frac{1-e}{t^e}$$
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