Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.5 The Chain Rule - 2.5 Exercises - Page 158: 14


$g'(θ) =-sin(2θ) $

Work Step by Step

Original Expression: $g(x)= cos^2(θ)$ $u = cos(θ)$ $g(u) = u^2$ Apply the chain rule: $g'(u)u'$ $g'(u) = 2(u)(-sin(θ))$ $g'(θ) = 2cos(θ)(-sin(θ))$ $g'(θ) =-2cos(θ)sin(θ) $ $g'(θ) =-sin(2θ) $, based on the double angle formula
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