Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.4 - The Chain Rule - 3.4 Exercises - Page 204: 14


$f'(t)=\pi t\cos\pi t+\sin\pi t$

Work Step by Step

$f(t)=t\sin\pi t$ Differentiate using the product rule: $f'(t)=(t)(\sin\pi t)'+(\sin\pi t)(t)'=...$ Now, use the chain rule to find $(\sin\pi t)'$: $...=(t)[(\cos\pi t)(\pi t)']+\sin\pi t=(t)(\pi\cos\pi t)+\sin\pi t=...$ $...=\pi t\cos\pi t+\sin\pi t$
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