Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises - Page 140: 12


$$ k'(\theta ) =2\theta \sin\theta (\sin\theta+\theta \cos\theta ) .$$

Work Step by Step

Recall the product rule: $(uv)'=u'v+uv'$ Recall that $(x^n)'=nx^{n-1}$ Recall that $(\sin x)'=\cos x$. Since $ k(\theta )= \theta^2 \sin^2 \theta $, then using the product rule, the derivative is giving by $$ k'(\theta )= (\theta^2)' \sin^2 \theta+\theta^2( \sin^2 \theta)'\\ =2\theta \sin^2 \theta+2\theta^2 \sin \theta \cos\theta\\ =2\theta \sin\theta (\sin\theta+\theta \cos\theta ) .$$
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.