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 - Page 146: 5


$4(x+\sin x)^{3}(1+\cos x)$

Work Step by Step

Let $ g(x)=u=x+\sin x $ and $ f(g(x))=y=(x+\sin x)^{4}=u^{4}$ Then, using the chain rule, we have $\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}=\frac{d}{du}(u^{4})\times\frac{d}{dx}(x+\sin x)$ $=4u^{3}\times(1+\cos x)$ $=4(x+\sin x)^{3}(1+\cos x)$
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.