Chapter 2.5, Problem 49E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

**Finding Derivatives** In Exercises 41–56, find the derivative of the function. State which differentiation rule(s) you used to find the derivative.

To determine

**To calculate:** The derivative of the provided function

Explanation

**Given Information:**

The provided function is

**Formula used:**

Product rule of differentiation:

General power rule of differentiation:

where

Constant rule of differentiation:

where

Simple power rule of differentiation:

where

Constant multiple rule of differentiation:

where

**Calculation:**

Consider the function

Differentiate the function

Apply the property of product rule of differentiation,

Apply the property of general power rule of differentiation,

Sect-2.1 P-1CPSect-2.1 P-2CPSect-2.1 P-3CPSect-2.1 P-4CPSect-2.1 P-5CPSect-2.1 P-6CPSect-2.1 P-7CPSect-2.1 P-1SWUSect-2.1 P-2SWUSect-2.1 P-3SWU

Sect-2.1 P-4SWUSect-2.1 P-5SWUSect-2.1 P-6SWUSect-2.1 P-7SWUSect-2.1 P-8SWUSect-2.1 P-9SWUSect-2.1 P-10SWUSect-2.1 P-11SWUSect-2.1 P-12SWUSect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10ESect-2.1 P-11ESect-2.1 P-12ESect-2.1 P-13ESect-2.1 P-14ESect-2.1 P-15ESect-2.1 P-16ESect-2.1 P-17ESect-2.1 P-18ESect-2.1 P-19ESect-2.1 P-20ESect-2.1 P-21ESect-2.1 P-22ESect-2.1 P-23ESect-2.1 P-24ESect-2.1 P-25ESect-2.1 P-26ESect-2.1 P-27ESect-2.1 P-28ESect-2.1 P-29ESect-2.1 P-30ESect-2.1 P-31ESect-2.1 P-32ESect-2.1 P-33ESect-2.1 P-34ESect-2.1 P-35ESect-2.1 P-36ESect-2.1 P-37ESect-2.1 P-38ESect-2.1 P-39ESect-2.1 P-40ESect-2.1 P-41ESect-2.1 P-42ESect-2.1 P-43ESect-2.1 P-44ESect-2.1 P-45ESect-2.1 P-46ESect-2.1 P-47ESect-2.1 P-48ESect-2.1 P-49ESect-2.1 P-50ESect-2.1 P-51ESect-2.1 P-52ESect-2.1 P-53ESect-2.1 P-54ESect-2.1 P-55ESect-2.1 P-56ESect-2.1 P-57ESect-2.1 P-58ESect-2.1 P-59ESect-2.1 P-60ESect-2.1 P-61ESect-2.1 P-62ESect-2.1 P-63ESect-2.1 P-64ESect-2.1 P-65ESect-2.1 P-66ESect-2.1 P-67ESect-2.1 P-68ESect-2.1 P-69ESect-2.1 P-70ESect-2.1 P-71ESect-2.1 P-72ESect-2.1 P-73ESect-2.2 P-1CPSect-2.2 P-2CPSect-2.2 P-3CPSect-2.2 P-5CPSect-2.2 P-6CPSect-2.2 P-7CPSect-2.2 P-8CPSect-2.2 P-9CPSect-2.2 P-10CPSect-2.2 P-11CPSect-2.2 P-1SWUSect-2.2 P-2SWUSect-2.2 P-3SWUSect-2.2 P-4SWUSect-2.2 P-5SWUSect-2.2 P-6SWUSect-2.2 P-7SWUSect-2.2 P-8SWUSect-2.2 P-9SWUSect-2.2 P-10SWUSect-2.2 P-1ESect-2.2 P-2ESect-2.2 P-3ESect-2.2 P-4ESect-2.2 P-5ESect-2.2 P-6ESect-2.2 P-7ESect-2.2 P-8ESect-2.2 P-9ESect-2.2 P-10ESect-2.2 P-11ESect-2.2 P-12ESect-2.2 P-13ESect-2.2 P-14ESect-2.2 P-15ESect-2.2 P-16ESect-2.2 P-17ESect-2.2 P-18ESect-2.2 P-19ESect-2.2 P-20ESect-2.2 P-21ESect-2.2 P-22ESect-2.2 P-23ESect-2.2 P-24ESect-2.2 P-25ESect-2.2 P-26ESect-2.2 P-27ESect-2.2 P-28ESect-2.2 P-29ESect-2.2 P-30ESect-2.2 P-31ESect-2.2 P-32ESect-2.2 P-33ESect-2.2 P-34ESect-2.2 P-35ESect-2.2 P-36ESect-2.2 P-37ESect-2.2 P-38ESect-2.2 P-39ESect-2.2 P-40ESect-2.2 P-41ESect-2.2 P-42ESect-2.2 P-43ESect-2.2 P-44ESect-2.2 P-45ESect-2.2 P-46ESect-2.2 P-47ESect-2.2 P-48ESect-2.2 P-49ESect-2.2 P-50ESect-2.2 P-51ESect-2.2 P-52ESect-2.2 P-53ESect-2.2 P-54ESect-2.2 P-55ESect-2.2 P-56ESect-2.2 P-57ESect-2.2 P-58ESect-2.2 P-59ESect-2.2 P-60ESect-2.2 P-61ESect-2.2 P-62ESect-2.2 P-63ESect-2.2 P-64ESect-2.2 P-65ESect-2.2 P-66ESect-2.2 P-67ESect-2.2 P-68ESect-2.2 P-69ESect-2.2 P-70ESect-2.2 P-71ESect-2.2 P-72ESect-2.2 P-73ESect-2.2 P-74ESect-2.2 P-75ESect-2.2 P-76ESect-2.2 P-77ESect-2.2 P-78ESect-2.2 P-79ESect-2.2 P-80ESect-2.2 P-81ESect-2.2 P-82ESect-2.2 P-83ESect-2.2 P-84ESect-2.3 P-1CPSect-2.3 P-2CPSect-2.3 P-3CPSect-2.3 P-4CPSect-2.3 P-5CPSect-2.3 P-6CPSect-2.3 P-7CPSect-2.3 P-8CPSect-2.3 P-1SWUSect-2.3 P-2SWUSect-2.3 P-3SWUSect-2.3 P-4SWUSect-2.3 P-5SWUSect-2.3 P-6SWUSect-2.3 P-7SWUSect-2.3 P-8SWUSect-2.3 P-9SWUSect-2.3 P-10SWUSect-2.3 P-11SWUSect-2.3 P-12SWUSect-2.3 P-1ESect-2.3 P-2ESect-2.3 P-3ESect-2.3 P-4ESect-2.3 P-5ESect-2.3 P-6ESect-2.3 P-7ESect-2.3 P-8ESect-2.3 P-9ESect-2.3 P-10ESect-2.3 P-11ESect-2.3 P-12ESect-2.3 P-13ESect-2.3 P-14ESect-2.3 P-15ESect-2.3 P-16ESect-2.3 P-17ESect-2.3 P-18ESect-2.3 P-19ESect-2.3 P-20ESect-2.3 P-21ESect-2.3 P-22ESect-2.3 P-23ESect-2.3 P-24ESect-2.3 P-25ESect-2.3 P-26ESect-2.3 P-27ESect-2.3 P-28ESect-2.3 P-29ESect-2.3 P-30ESect-2.3 P-31ESect-2.3 P-32ESect-2.3 P-33ESect-2.3 P-34ESect-2.3 P-35ESect-2.3 P-36ESect-2.3 P-37ESect-2.3 P-38ESect-2.3 P-39ESect-2.3 P-40ESect-2.3 P-41ESect-2.3 P-42ESect-2.3 P-43ESect-2.3 P-44ESect-2.4 P-1CPSect-2.4 P-2CPSect-2.4 P-3CPSect-2.4 P-4CPSect-2.4 P-5CPSect-2.4 P-6CPSect-2.4 P-7CPSect-2.4 P-8CPSect-2.4 P-1SWUSect-2.4 P-2SWUSect-2.4 P-3SWUSect-2.4 P-4SWUSect-2.4 P-5SWUSect-2.4 P-6SWUSect-2.4 P-7SWUSect-2.4 P-8SWUSect-2.4 P-9SWUSect-2.4 P-10SWUSect-2.4 P-11SWUSect-2.4 P-12SWUSect-2.4 P-13SWUSect-2.4 P-14SWUSect-2.4 P-1ESect-2.4 P-2ESect-2.4 P-3ESect-2.4 P-4ESect-2.4 P-5ESect-2.4 P-6ESect-2.4 P-7ESect-2.4 P-8ESect-2.4 P-9ESect-2.4 P-10ESect-2.4 P-11ESect-2.4 P-12ESect-2.4 P-13ESect-2.4 P-14ESect-2.4 P-15ESect-2.4 P-16ESect-2.4 P-17ESect-2.4 P-18ESect-2.4 P-19ESect-2.4 P-20ESect-2.4 P-21ESect-2.4 P-22ESect-2.4 P-23ESect-2.4 P-24ESect-2.4 P-25ESect-2.4 P-26ESect-2.4 P-27ESect-2.4 P-28ESect-2.4 P-29ESect-2.4 P-30ESect-2.4 P-31ESect-2.4 P-32ESect-2.4 P-33ESect-2.4 P-34ESect-2.4 P-35ESect-2.4 P-36ESect-2.4 P-37ESect-2.4 P-38ESect-2.4 P-39ESect-2.4 P-40ESect-2.4 P-41ESect-2.4 P-42ESect-2.4 P-43ESect-2.4 P-44ESect-2.4 P-45ESect-2.4 P-46ESect-2.4 P-47ESect-2.4 P-48ESect-2.4 P-49ESect-2.4 P-50ESect-2.4 P-51ESect-2.4 P-52ESect-2.4 P-53ESect-2.4 P-54ESect-2.4 P-55ESect-2.4 P-56ESect-2.4 P-57ESect-2.4 P-58ESect-2.4 P-59ESect-2.4 P-60ESect-2.4 P-61ESect-2.4 P-62ESect-2.4 P-63ESect-2.4 P-64ESect-2.4 P-65ESect-2.4 P-66ESect-2.4 P-67ESect-2.4 P-68ESect-2.4 P-69ESect-2.4 P-70ESect-2.4 P-71ESect-2.4 P-72ESect-2.4 P-73ESect-2.4 P-74ESect-2.4 P-75ESect-2.4 P-76ESect-2.4 P-77ESect-2.4 P-1QYSect-2.4 P-2QYSect-2.4 P-3QYSect-2.4 P-4QYSect-2.4 P-5QYSect-2.4 P-6QYSect-2.4 P-7QYSect-2.4 P-8QYSect-2.4 P-9QYSect-2.4 P-10QYSect-2.4 P-11QYSect-2.4 P-12QYSect-2.4 P-13QYSect-2.4 P-14QYSect-2.4 P-15QYSect-2.4 P-16QYSect-2.4 P-17QYSect-2.4 P-18QYSect-2.4 P-19QYSect-2.4 P-20QYSect-2.4 P-21QYSect-2.4 P-22QYSect-2.4 P-23QYSect-2.5 P-1CPSect-2.5 P-2CPSect-2.5 P-3CPSect-2.5 P-4CPSect-2.5 P-5CPSect-2.5 P-6CPSect-2.5 P-7CPSect-2.5 P-8CPSect-2.5 P-1SWUSect-2.5 P-2SWUSect-2.5 P-3SWUSect-2.5 P-4SWUSect-2.5 P-5SWUSect-2.5 P-6SWUSect-2.5 P-7SWUSect-2.5 P-8SWUSect-2.5 P-9SWUSect-2.5 P-10SWUSect-2.5 P-1ESect-2.5 P-2ESect-2.5 P-3ESect-2.5 P-4ESect-2.5 P-5ESect-2.5 P-6ESect-2.5 P-7ESect-2.5 P-8ESect-2.5 P-9ESect-2.5 P-10ESect-2.5 P-11ESect-2.5 P-12ESect-2.5 P-13ESect-2.5 P-14ESect-2.5 P-15ESect-2.5 P-16ESect-2.5 P-17ESect-2.5 P-18ESect-2.5 P-19ESect-2.5 P-20ESect-2.5 P-21ESect-2.5 P-22ESect-2.5 P-23ESect-2.5 P-24ESect-2.5 P-25ESect-2.5 P-26ESect-2.5 P-27ESect-2.5 P-28ESect-2.5 P-29ESect-2.5 P-30ESect-2.5 P-31ESect-2.5 P-32ESect-2.5 P-33ESect-2.5 P-34ESect-2.5 P-35ESect-2.5 P-36ESect-2.5 P-37ESect-2.5 P-38ESect-2.5 P-39ESect-2.5 P-40ESect-2.5 P-41ESect-2.5 P-42ESect-2.5 P-43ESect-2.5 P-44ESect-2.5 P-45ESect-2.5 P-46ESect-2.5 P-47ESect-2.5 P-48ESect-2.5 P-49ESect-2.5 P-50ESect-2.5 P-51ESect-2.5 P-52ESect-2.5 P-53ESect-2.5 P-54ESect-2.5 P-55ESect-2.5 P-56ESect-2.5 P-57ESect-2.5 P-58ESect-2.5 P-59ESect-2.5 P-60ESect-2.5 P-61ESect-2.5 P-62ESect-2.5 P-63ESect-2.5 P-64ESect-2.5 P-65ESect-2.5 P-66ESect-2.5 P-67ESect-2.5 P-68ESect-2.5 P-69ESect-2.5 P-70ESect-2.5 P-71ESect-2.5 P-72ESect-2.5 P-73ESect-2.6 P-1CPSect-2.6 P-2CPSect-2.6 P-3CPSect-2.6 P-4CPSect-2.6 P-5CPSect-2.6 P-6CPSect-2.6 P-1SWUSect-2.6 P-2SWUSect-2.6 P-3SWUSect-2.6 P-4SWUSect-2.6 P-5SWUSect-2.6 P-6SWUSect-2.6 P-7SWUSect-2.6 P-8SWUSect-2.6 P-9SWUSect-2.6 P-10SWUSect-2.6 P-1ESect-2.6 P-2ESect-2.6 P-3ESect-2.6 P-4ESect-2.6 P-5ESect-2.6 P-6ESect-2.6 P-7ESect-2.6 P-8ESect-2.6 P-9ESect-2.6 P-10ESect-2.6 P-11ESect-2.6 P-12ESect-2.6 P-13ESect-2.6 P-14ESect-2.6 P-15ESect-2.6 P-16ESect-2.6 P-17ESect-2.6 P-18ESect-2.6 P-19ESect-2.6 P-20ESect-2.6 P-21ESect-2.6 P-22ESect-2.6 P-23ESect-2.6 P-24ESect-2.6 P-25ESect-2.6 P-26ESect-2.6 P-27ESect-2.6 P-28ESect-2.6 P-29ESect-2.6 P-30ESect-2.6 P-31ESect-2.6 P-32ESect-2.6 P-33ESect-2.6 P-34ESect-2.6 P-35ESect-2.6 P-36ESect-2.6 P-37ESect-2.6 P-38ESect-2.6 P-39ESect-2.6 P-40ESect-2.6 P-41ESect-2.6 P-42ESect-2.6 P-43ESect-2.6 P-44ESect-2.6 P-45ESect-2.7 P-1CPSect-2.7 P-2CPSect-2.7 P-3CPSect-2.7 P-4CPSect-2.7 P-5CPSect-2.7 P-6CPSect-2.7 P-1SWUSect-2.7 P-2SWUSect-2.7 P-3SWUSect-2.7 P-4SWUSect-2.7 P-5SWUSect-2.7 P-6SWUSect-2.7 P-7SWUSect-2.7 P-8SWUSect-2.7 P-9SWUSect-2.7 P-1ESect-2.7 P-2ESect-2.7 P-3ESect-2.7 P-4ESect-2.7 P-5ESect-2.7 P-6ESect-2.7 P-7ESect-2.7 P-8ESect-2.7 P-9ESect-2.7 P-10ESect-2.7 P-11ESect-2.7 P-12ESect-2.7 P-13ESect-2.7 P-14ESect-2.7 P-15ESect-2.7 P-16ESect-2.7 P-17ESect-2.7 P-18ESect-2.7 P-19ESect-2.7 P-20ESect-2.7 P-21ESect-2.7 P-22ESect-2.7 P-23ESect-2.7 P-24ESect-2.7 P-25ESect-2.7 P-26ESect-2.7 P-27ESect-2.7 P-28ESect-2.7 P-29ESect-2.7 P-30ESect-2.7 P-31ESect-2.7 P-32ESect-2.7 P-33ESect-2.7 P-34ESect-2.7 P-35ESect-2.7 P-36ESect-2.7 P-37ESect-2.7 P-38ESect-2.7 P-39ESect-2.7 P-40ESect-2.7 P-41ESect-2.7 P-42ESect-2.7 P-43ESect-2.7 P-44ESect-2.7 P-45ESect-2.7 P-46ESect-2.7 P-47ESect-2.7 P-48ESect-2.7 P-49ESect-2.8 P-1CPSect-2.8 P-2CPSect-2.8 P-3CPSect-2.8 P-4CPSect-2.8 P-1SWUSect-2.8 P-2SWUSect-2.8 P-3SWUSect-2.8 P-4SWUSect-2.8 P-5SWUSect-2.8 P-6SWUSect-2.8 P-7SWUSect-2.8 P-8SWUSect-2.8 P-9SWUSect-2.8 P-10SWUSect-2.8 P-1ESect-2.8 P-2ESect-2.8 P-3ESect-2.8 P-4ESect-2.8 P-5ESect-2.8 P-6ESect-2.8 P-7ESect-2.8 P-8ESect-2.8 P-9ESect-2.8 P-10ESect-2.8 P-11ESect-2.8 P-12ESect-2.8 P-13ESect-2.8 P-14ESect-2.8 P-15ESect-2.8 P-16ESect-2.8 P-17ESect-2.8 P-18ESect-2.8 P-19ESect-2.8 P-20ESect-2.8 P-21ESect-2.8 P-22ESect-2.8 P-23ESect-2.8 P-24ESect-2.8 P-25ESect-2.8 P-26ECh-2 P-1RECh-2 P-2RECh-2 P-3RECh-2 P-4RECh-2 P-5RECh-2 P-6RECh-2 P-7RECh-2 P-8RECh-2 P-9RECh-2 P-10RECh-2 P-11RECh-2 P-12RECh-2 P-13RECh-2 P-14RECh-2 P-15RECh-2 P-16RECh-2 P-17RECh-2 P-18RECh-2 P-19RECh-2 P-20RECh-2 P-21RECh-2 P-22RECh-2 P-23RECh-2 P-24RECh-2 P-25RECh-2 P-26RECh-2 P-27RECh-2 P-28RECh-2 P-29RECh-2 P-30RECh-2 P-31RECh-2 P-32RECh-2 P-33RECh-2 P-34RECh-2 P-35RECh-2 P-36RECh-2 P-37RECh-2 P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-55RECh-2 P-56RECh-2 P-57RECh-2 P-58RECh-2 P-59RECh-2 P-60RECh-2 P-61RECh-2 P-62RECh-2 P-63RECh-2 P-64RECh-2 P-65RECh-2 P-66RECh-2 P-67RECh-2 P-68RECh-2 P-69RECh-2 P-70RECh-2 P-71RECh-2 P-72RECh-2 P-73RECh-2 P-74RECh-2 P-75RECh-2 P-76RECh-2 P-77RECh-2 P-78RECh-2 P-79RECh-2 P-80RECh-2 P-81RECh-2 P-82RECh-2 P-83RECh-2 P-84RECh-2 P-85RECh-2 P-86RECh-2 P-87RECh-2 P-88RECh-2 P-89RECh-2 P-90RECh-2 P-91RECh-2 P-92RECh-2 P-93RECh-2 P-94RECh-2 P-95RECh-2 P-96RECh-2 P-97RECh-2 P-98RECh-2 P-99RECh-2 P-100RECh-2 P-101RECh-2 P-102RECh-2 P-103RECh-2 P-104RECh-2 P-105RECh-2 P-106RECh-2 P-107RECh-2 P-108RECh-2 P-109RECh-2 P-110RECh-2 P-111RECh-2 P-112RECh-2 P-113RECh-2 P-114RECh-2 P-1TYSCh-2 P-2TYSCh-2 P-3TYSCh-2 P-4TYSCh-2 P-5TYSCh-2 P-6TYSCh-2 P-7TYSCh-2 P-8TYSCh-2 P-9TYSCh-2 P-10TYSCh-2 P-11TYSCh-2 P-12TYSCh-2 P-13TYSCh-2 P-14TYSCh-2 P-15TYSCh-2 P-16TYSCh-2 P-17TYSCh-2 P-18TYSCh-2 P-19TYSCh-2 P-20TYSCh-2 P-21TYSCh-2 P-22TYS

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