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: 8

Answer

First Derivative: $s'=\frac{2}{t^{2}}-\frac{8}{t^{3}}$ Second Derivative: $s''=-\frac{4}{t^{3}}+\frac{24}{t^{4}}$

Work Step by Step

Using the Power Rule: First Derivative: $s=-2t^{-1}+\frac{4}{t^{2}}$ $s'=(-1)(-2)t^{-1-1}+(-2)(4)t^{-2-1}$ $s'=2t^{-2}-8t^{-3}$ $s'=\frac{2}{t^{2}}-\frac{8}{t^{3}}$ Second Derivative: $s'=2t^{-2}-8t^{-3}$ $s''=(-2)(2)t^{-2-1}-(-3)(8)t^{-3-1}$ $s''=-4t^{-3}+24t^{-4}$ $s''=-\frac{4}{t^{3}}+\frac{24}{t^{4}}$
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