Thomas' Calculus 13th Edition

Published by Pearson

Chapter 3: Derivatives - Section 3.3 Differentiation Rules - Exercises 3.3: 11

Answer

First Derivative: $r'=\frac{-2}{3s^{3}}+\frac{5}{2s^{2}}$ Second Derivative: $r''=\frac{2}{s^{4}}-\frac{5}{s^{3}}$

Work Step by Step

Using the Power Rule: First Derivative: $r=\frac{1}{3s^{2}}-\frac{5}{2s}$ $r'=(-2)(\frac{1}{3})s^{-2-1}-(-1)(\frac{5}{2})s^{-1-1}$ $r'=\frac{-2}{3}s^{-3}+\frac{5}{2}s^{-2}$ $r'=\frac{-2}{3s^{3}}+\frac{5}{2s^{2}}$ Second Derivative: $r'=\frac{-2}{3}s^{-3}+\frac{5}{2}s^{-2}$ $r''=(-3)\frac{-2}{3}s^{-3-1}+(-2)\frac{5}{2}s^{-2-1}$ $r''=2s^{-4}-5s^{-3}$ $r''=\frac{2}{s^{4}}-\frac{5}{s^{3}}$

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