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: 41

Answer

$f'(\theta) = 4\theta \csc (9 - 2\theta ^2) \cot (9 - 2\theta ^2)$

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 $u = 9 - 2\theta ^2$ $f(u) = \csc u$ Derivate the function: $f'(u) = -u' \csc u \cot u$ Now let's find u' $u' = -4\theta$ Then undo the substitution, simplify and get the answer: $f'(\theta) = -(-4\theta) \csc (9 - 2\theta ^2) \cot (9 - 2\theta ^2)$ $f'(\theta) = 4\theta \csc (9 - 2\theta ^2) \cot (9 - 2\theta ^2)$
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.