University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 3 - Section 3.5 - Derivatives of Trigonometric Functions - Exercises - Page 151: 9


$y' = e^{-x}secx(xtanx -x +1)$

Work Step by Step

$y = xe^{-x}secx$ $y = e^{-x}(x\ secx)$ $y' = -e^{x}(x\ secx) + e^{-x}(secx + x\ secx\ tanx)$ $y' = -e^{-x}\ x\ secx +e^{-x}secx + e^{-x}\ x\ secx\ tanx$ $y' = e^{-x}secx(xtanx -x +1)$
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