Answer
$$f'(t)=\sin\pi t+\pi t\cos\pi t$$
Work Step by Step
$$f'(t)=(t\sin \pi t)'=t'\cdot\sin\pi t+t\cdot(\sin\pi t)'=
1\cdot\sin\pi t+t\cdot\cos\pi t(\pi t)'=
\sin\pi t+t\cos\pi t\cdot\pi=\sin\pi t+\pi t\cos\pi t$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 2 - Derivatives - 2.5 The Chain Rule - 2.5 Exercises - Page 158: 16
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