Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.3 - Derivatives of Trigonometric Functions - 3.3 Exercises: 7

Answer

$y'=-c\sin t+t^{2}\cos t+2t\sin t$

Work Step by Step

$y=c\cos t+t^{2}\sin t$ (Here, $c$ is a constant) Differentiate each term: $y'=(c\cos t)'+(t^{2}\sin t)'$ Use the product rule to find $(t^{2}\sin t)'$: $y'=-c\sin t+(t^{2})(\sin t)'+(\sin t)(t^{2})'=...$ $...=-c\sin t+t^{2}\cos t+2t\sin t$
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