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: 7

Answer

First Derivative: $w'=\frac{-6}{z^{3}}+\frac{1}{z^{2}}$ Second Derivative: $w''=\frac{18}{z^{4}}-\frac{2}{z^{3}}$

Work Step by Step

Using the power rule: First Derivative: $w=3z^{-2}-\frac{1}{z}$ $w'=(-2)(3)z^{-2-1}-(-1)z^{-1-1}$ $w'=-6z^{-3}+z^{-2}$ $w'=\frac{-6}{z^{3}}+\frac{1}{z^{2}}$ Second Derivative: $w'=-6z^{-3}+z^{-2}$ $w''=(-3)(-6)z^{-3-1}+(-2)z^{-2-1}$ $w''=18z^{-4}-2z^{-3}$ $w''=\frac{18}{z^{4}}-\frac{2}{z^{3}}$
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