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: 4

Answer

First Derivative: w' = 21$z^{6}$ - 21$z^{2}$ + 42$z$ Second Derivative: w'' = 126$z^{5}$ - 42$z$ + 42

Work Step by Step

Using the Power Rule: First Derivative: w = 3$z^{7}$ - 7$z^{3}$ + 21$z^{2}$ w' = (7)(3)$z^{7-1}$ - (3)(7)$z^{3-1}$ + (2)(21)$z^{2-1}$ w' = 21$z^{6}$ - 21$z^{2}$ + 42$z$ Second Derivative: w' = 21$z^{6}$ - 21$z^{2}$ + 42$z$ w'' = (6)(21)$z^{6-1}$ - (2)(21)$z^{2-1}$ + (1)42$z^{1-1}$ w'' = 126$z^{5}$ - 42$z$ + 42
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