Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises: 17

Answer

$f'(\theta) = -4 \cos^3\theta\sin\theta$

Work Step by Step

In order to derivate this function you have to apply the chain rule Let's make an «u» substitution to make it easier $u = \cos \theta $ $f(u) = u^4$ Derivate the function: $f'(u) = 4u^3u'$ Now let's find u' $u' = -\sin \theta$ Then undo the substitution, simplify and get the answer: $f'(\theta) = -4 \cos^3\theta\sin\theta$
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.