Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.3 Differentiation Rules - Exercises 3.3: 3

Answer

First Derivative: s' = 15$t^{2}$ - 15$t^{4}$ Second Derivative: s'' = 30$t$ - 60$t^{3}$

Work Step by Step

Using the power rule: Work with the first and second term separately First Derivative: s = 5$t^{3}$ - 3$t^{5}$ s' = (3)(5)$t^{2}$ - (5)(3)$t^{4}$ s' = 15$t^{2}$ - 15$t^{4}$ Second Derivative: s' = 15$t^{2}$ - 15$t^{4}$ s'' = (2)(15)$t$ - (4)(15)$t^{3}$ s'' = 30$t$ - 60$t^{3}$
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