Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.7 The Chain Rule - 3.7 Exercises - Page 191: 28


$y' = e^{tan (t)} \times sec^2(t)$

Work Step by Step

$y = e^{tan (t)}$ $y' = (e^{tan (t)})'$ The inner function is $g(t) = tan(t)$ and the outer function is $f(u) = e^u$ $f'(u) = e^u$ $y' = (e^{tan (t)})' = e^{g(t)}\times g'(t) = e^{tan (t)} \times sec^2(t)$
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