Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.6 The Chain Rule - Exercises Set 2.6: 55

Answer

$$\frac{dy}{d\theta}=3\cot^2\theta\csc^2\theta$$

Work Step by Step

$$\frac{dy}{d\theta}=\frac{d}{d\theta}(\cot^3(\pi-\theta))=3\cot^2(\pi-\theta)\frac{d}{d\theta}(\cot(\pi-\theta))= 3\cot^2(\pi-\theta)\cdot(-\csc^2(\pi-\theta))\frac{d}{d\theta}(\pi-\theta)=-3\cot^2(\pi-\theta)\csc^2(\pi-\theta)\cdot(-1)=3\cot^2(\pi-\theta)\csc^2(\pi-\theta)=3(-\cot\theta)^2\csc^2\theta=3\cot^2\theta\csc^2\theta$$
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.