University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 202: 15


$s'=5\sec t(\sec t+\tan t)^5$

Work Step by Step

Given that $s=(\sec t+\tan t)^5$ Apply derivative rules of differentiation: $f(x)=p'(x)q(x)+p(x)q'(x)$ $y'=\dfrac{d}{dx}[(\sec t+\tan t)^5]$ $=5(\sec t+\tan t)^4\dfrac{d}{dx}(\sec t+\tan t)$ $=5(\sec t+\tan t)^4(\sec t\tan t+\sec^2 t)$ Hence, $s'=5\sec t(\sec t+\tan t)^5$
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