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: 14

Answer

$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
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.