University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 3 - Practice Exercises - Page 202: 8


$y'=2(-1-\dfrac{csc\theta}{2}-\dfrac{\theta^2}{4})(\dfrac{csc\theta \cot \theta}{2}- \dfrac{\theta}{2})$

Work Step by Step

Given that $y=(-1-\dfrac{csc\theta}{2}-\dfrac{\theta^2}{4})^2$ Apply derivative rules of differentiation: $f(x)=p'(x)q(x)+p(x)q'(x)$ $y'=\frac{d}{dx}[(-1-\dfrac{csc\theta}{2}-\dfrac{\theta^2}{4})^2]$ $=2(-1-\dfrac{csc\theta}{2}-\dfrac{\theta^2}{4})(-1-\dfrac{csc\theta}{2}-\dfrac{\theta^2}{4})'$ Hence, $y'=2(-1-\dfrac{csc\theta}{2}-\dfrac{\theta^2}{4})(\dfrac{csc\theta \cot \theta}{2}- \dfrac{\theta}{2})$
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.