Chapter 13.3, Problem 27E

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11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

Finding Partial Derivatives In Exercises 11-40, find both first partial derivatives.

To determine

**To calculate:** The partial derivative for the function *x* and *y*.

Explanation

**Given:**

The function,

**Formula used:**

The partial derivative of the function *x* is,

The partial derivative of the function *y* is,

The derivative of,

**Calculation:**

Consider,

Now,

Differentiate the function with respect to *x* as follows,

Sect-13.1 P-1ESect-13.1 P-2ESect-13.1 P-3ESect-13.1 P-4ESect-13.1 P-5ESect-13.1 P-6ESect-13.1 P-7ESect-13.1 P-8ESect-13.1 P-9ESect-13.1 P-10E

Sect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.1 P-41ESect-13.1 P-42ESect-13.1 P-43ESect-13.1 P-44ESect-13.1 P-45ESect-13.1 P-46ESect-13.1 P-47ESect-13.1 P-48ESect-13.1 P-49ESect-13.1 P-50ESect-13.1 P-51ESect-13.1 P-52ESect-13.1 P-53ESect-13.1 P-54ESect-13.1 P-55ESect-13.1 P-56ESect-13.1 P-57ESect-13.1 P-58ESect-13.1 P-59ESect-13.1 P-60ESect-13.1 P-61ESect-13.1 P-62ESect-13.1 P-63ESect-13.1 P-64ESect-13.1 P-65ESect-13.1 P-66ESect-13.1 P-67ESect-13.1 P-68ESect-13.1 P-69ESect-13.1 P-70ESect-13.1 P-71ESect-13.1 P-72ESect-13.1 P-73ESect-13.1 P-74ESect-13.1 P-75ESect-13.1 P-76ESect-13.1 P-77ESect-13.1 P-78ESect-13.1 P-79ESect-13.1 P-80ESect-13.1 P-81ESect-13.1 P-82ESect-13.1 P-83ESect-13.1 P-84ESect-13.1 P-85ESect-13.1 P-86ESect-13.1 P-87ESect-13.1 P-88ESect-13.1 P-89ESect-13.1 P-90ESect-13.1 P-91ESect-13.1 P-92ESect-13.1 P-93ESect-13.1 P-94ESect-13.1 P-95ESect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 P-33ESect-13.2 P-34ESect-13.2 P-35ESect-13.2 P-36ESect-13.2 P-37ESect-13.2 P-38ESect-13.2 P-39ESect-13.2 P-40ESect-13.2 P-41ESect-13.2 P-42ESect-13.2 P-43ESect-13.2 P-44ESect-13.2 P-45ESect-13.2 P-46ESect-13.2 P-47ESect-13.2 P-48ESect-13.2 P-49ESect-13.2 P-50ESect-13.2 P-51ESect-13.2 P-52ESect-13.2 P-53ESect-13.2 P-54ESect-13.2 P-55ESect-13.2 P-56ESect-13.2 P-57ESect-13.2 P-58ESect-13.2 P-59ESect-13.2 P-60ESect-13.2 P-61ESect-13.2 P-62ESect-13.2 P-63ESect-13.2 P-64ESect-13.2 P-65ESect-13.2 P-66ESect-13.2 P-67ESect-13.2 P-68ESect-13.2 P-69ESect-13.2 P-70ESect-13.2 P-71ESect-13.2 P-72ESect-13.2 P-73ESect-13.2 P-74ESect-13.2 P-75ESect-13.2 P-76ESect-13.2 P-77ESect-13.2 P-78ESect-13.2 P-79ESect-13.2 P-80ESect-13.2 P-81ESect-13.2 P-82ESect-13.2 P-83ESect-13.2 P-84ESect-13.2 P-85ESect-13.2 P-86ESect-13.3 P-1ESect-13.3 P-2ESect-13.3 P-3ESect-13.3 P-4ESect-13.3 P-5ESect-13.3 P-6ESect-13.3 P-7ESect-13.3 P-8ESect-13.3 P-9ESect-13.3 P-10ESect-13.3 P-11ESect-13.3 P-12ESect-13.3 P-13ESect-13.3 P-14ESect-13.3 P-15ESect-13.3 P-16ESect-13.3 P-17ESect-13.3 P-18ESect-13.3 P-19ESect-13.3 P-20ESect-13.3 P-21ESect-13.3 P-22ESect-13.3 P-23ESect-13.3 P-24ESect-13.3 P-25ESect-13.3 P-26ESect-13.3 P-27ESect-13.3 P-28ESect-13.3 P-29ESect-13.3 P-30ESect-13.3 P-31ESect-13.3 P-32ESect-13.3 P-33ESect-13.3 P-34ESect-13.3 P-35ESect-13.3 P-36ESect-13.3 P-37ESect-13.3 P-38ESect-13.3 P-39ESect-13.3 P-40ESect-13.3 P-41ESect-13.3 P-42ESect-13.3 P-43ESect-13.3 P-44ESect-13.3 P-45ESect-13.3 P-46ESect-13.3 P-47ESect-13.3 P-48ESect-13.3 P-49ESect-13.3 P-50ESect-13.3 P-51ESect-13.3 P-52ESect-13.3 P-53ESect-13.3 P-54ESect-13.3 P-55ESect-13.3 P-56ESect-13.3 P-57ESect-13.3 P-58ESect-13.3 P-59ESect-13.3 P-60ESect-13.3 P-61ESect-13.3 P-62ESect-13.3 P-63ESect-13.3 P-64ESect-13.3 P-65ESect-13.3 P-66ESect-13.3 P-67ESect-13.3 P-68ESect-13.3 P-69ESect-13.3 P-70ESect-13.3 P-71ESect-13.3 P-72ESect-13.3 P-73ESect-13.3 P-74ESect-13.3 P-75ESect-13.3 P-76ESect-13.3 P-77ESect-13.3 P-78ESect-13.3 P-79ESect-13.3 P-80ESect-13.3 P-81ESect-13.3 P-82ESect-13.3 P-83ESect-13.3 P-84ESect-13.3 P-85ESect-13.3 P-86ESect-13.3 P-87ESect-13.3 P-88ESect-13.3 P-89ESect-13.3 P-90ESect-13.3 P-91ESect-13.3 P-92ESect-13.3 P-93ESect-13.3 P-94ESect-13.3 P-95ESect-13.3 P-96ESect-13.3 P-97ESect-13.3 P-98ESect-13.3 P-99ESect-13.3 P-100ESect-13.3 P-101ESect-13.3 P-102ESect-13.3 P-103ESect-13.3 P-104ESect-13.3 P-105ESect-13.3 P-106ESect-13.3 P-107ESect-13.3 P-108ESect-13.3 P-109ESect-13.3 P-110ESect-13.3 P-111ESect-13.3 P-112ESect-13.3 P-113ESect-13.3 P-114ESect-13.3 P-115ESect-13.3 P-116ESect-13.3 P-117ESect-13.3 P-118ESect-13.3 P-119ESect-13.3 P-120ESect-13.3 P-121ESect-13.3 P-122ESect-13.3 P-123ESect-13.3 P-124ESect-13.3 P-125ESect-13.3 P-126ESect-13.3 P-127ESect-13.3 P-128ESect-13.3 P-129ESect-13.3 P-130ESect-13.3 P-131ESect-13.4 P-1ESect-13.4 P-2ESect-13.4 P-3ESect-13.4 P-4ESect-13.4 P-5ESect-13.4 P-6ESect-13.4 P-7ESect-13.4 P-8ESect-13.4 P-9ESect-13.4 P-10ESect-13.4 P-11ESect-13.4 P-12ESect-13.4 P-13ESect-13.4 P-14ESect-13.4 P-15ESect-13.4 P-16ESect-13.4 P-17ESect-13.4 P-18ESect-13.4 P-19ESect-13.4 P-20ESect-13.4 P-21ESect-13.4 P-22ESect-13.4 P-23ESect-13.4 P-24ESect-13.4 P-25ESect-13.4 P-26ESect-13.4 P-27ESect-13.4 P-28ESect-13.4 P-29ESect-13.4 P-30ESect-13.4 P-31ESect-13.4 P-32ESect-13.4 P-33ESect-13.4 P-34ESect-13.4 P-35ESect-13.4 P-36ESect-13.4 P-37ESect-13.4 P-38ESect-13.4 P-39ESect-13.4 P-40ESect-13.5 P-1ESect-13.5 P-2ESect-13.5 P-3ESect-13.5 P-4ESect-13.5 P-5ESect-13.5 P-6ESect-13.5 P-7ESect-13.5 P-8ESect-13.5 P-9ESect-13.5 P-10ESect-13.5 P-11ESect-13.5 P-12ESect-13.5 P-13ESect-13.5 P-14ESect-13.5 P-15ESect-13.5 P-16ESect-13.5 P-17ESect-13.5 P-18ESect-13.5 P-19ESect-13.5 P-20ESect-13.5 P-21ESect-13.5 P-22ESect-13.5 P-23ESect-13.5 P-24ESect-13.5 P-25ESect-13.5 P-26ESect-13.5 P-27ESect-13.5 P-28ESect-13.5 P-29ESect-13.5 P-30ESect-13.5 P-31ESect-13.5 P-32ESect-13.5 P-33ESect-13.5 P-34ESect-13.5 P-35ESect-13.5 P-36ESect-13.5 P-37ESect-13.5 P-38ESect-13.5 P-39ESect-13.5 P-40ESect-13.5 P-41ESect-13.5 P-42ESect-13.5 P-43ESect-13.5 P-44ESect-13.5 P-45ESect-13.5 P-46ESect-13.5 P-47ESect-13.5 P-48ESect-13.5 P-49ESect-13.5 P-50ESect-13.5 P-51ESect-13.5 P-52ESect-13.5 P-53ESect-13.5 P-54ESect-13.5 P-55ESect-13.6 P-1ESect-13.6 P-2ESect-13.6 P-3ESect-13.6 P-4ESect-13.6 P-5ESect-13.6 P-6ESect-13.6 P-7ESect-13.6 P-8ESect-13.6 P-9ESect-13.6 P-10ESect-13.6 P-11ESect-13.6 P-12ESect-13.6 P-13ESect-13.6 P-14ESect-13.6 P-15ESect-13.6 P-16ESect-13.6 P-17ESect-13.6 P-18ESect-13.6 P-19ESect-13.6 P-20ESect-13.6 P-21ESect-13.6 P-22ESect-13.6 P-23ESect-13.6 P-24ESect-13.6 P-25ESect-13.6 P-26ESect-13.6 P-27ESect-13.6 P-28ESect-13.6 P-29ESect-13.6 P-30ESect-13.6 P-31ESect-13.6 P-32ESect-13.6 P-33ESect-13.6 P-34ESect-13.6 P-35ESect-13.6 P-36ESect-13.6 P-37ESect-13.6 P-38ESect-13.6 P-39ESect-13.6 P-40ESect-13.6 P-41ESect-13.6 P-42ESect-13.6 P-43ESect-13.6 P-44ESect-13.6 P-45ESect-13.6 P-46ESect-13.6 P-47ESect-13.6 P-48ESect-13.6 P-49ESect-13.6 P-50ESect-13.6 P-51ESect-13.6 P-52ESect-13.6 P-53ESect-13.6 P-54ESect-13.6 P-55ESect-13.6 P-56ESect-13.6 P-57ESect-13.6 P-58ESect-13.6 P-59ESect-13.6 P-60ESect-13.6 P-61ESect-13.6 P-62ESect-13.6 P-63ESect-13.6 P-64ESect-13.6 P-65ESect-13.6 P-66ESect-13.6 P-67ESect-13.6 P-68ESect-13.7 P-1ESect-13.7 P-2ESect-13.7 P-3ESect-13.7 P-4ESect-13.7 P-5ESect-13.7 P-6ESect-13.7 P-7ESect-13.7 P-8ESect-13.7 P-9ESect-13.7 P-10ESect-13.7 P-11ESect-13.7 P-12ESect-13.7 P-13ESect-13.7 P-14ESect-13.7 P-15ESect-13.7 P-16ESect-13.7 P-17ESect-13.7 P-18ESect-13.7 P-19ESect-13.7 P-20ESect-13.7 P-21ESect-13.7 P-22ESect-13.7 P-23ESect-13.7 P-24ESect-13.7 P-25ESect-13.7 P-26ESect-13.7 P-27ESect-13.7 P-28ESect-13.7 P-29ESect-13.7 P-30ESect-13.7 P-31ESect-13.7 P-32ESect-13.7 P-33ESect-13.7 P-34ESect-13.7 P-35ESect-13.7 P-36ESect-13.7 P-37ESect-13.7 P-38ESect-13.7 P-39ESect-13.7 P-40ESect-13.7 P-41ESect-13.7 P-42ESect-13.7 P-43ESect-13.7 P-44ESect-13.7 P-45ESect-13.7 P-46ESect-13.7 P-47ESect-13.7 P-48ESect-13.7 P-49ESect-13.7 P-50ESect-13.7 P-51ESect-13.7 P-52ESect-13.7 P-53ESect-13.7 P-54ESect-13.7 P-55ESect-13.7 P-56ESect-13.7 P-57ESect-13.7 P-58ESect-13.7 P-59ESect-13.7 P-60ESect-13.7 P-61ESect-13.7 P-62ESect-13.7 P-63ESect-13.7 P-64ESect-13.8 P-1ESect-13.8 P-2ESect-13.8 P-3ESect-13.8 P-4ESect-13.8 P-5ESect-13.8 P-6ESect-13.8 P-7ESect-13.8 P-8ESect-13.8 P-9ESect-13.8 P-10ESect-13.8 P-11ESect-13.8 P-12ESect-13.8 P-13ESect-13.8 P-14ESect-13.8 P-15ESect-13.8 P-16ESect-13.8 P-17ESect-13.8 P-18ESect-13.8 P-19ESect-13.8 P-20ESect-13.8 P-21ESect-13.8 P-22ESect-13.8 P-23ESect-13.8 P-24ESect-13.8 P-25ESect-13.8 P-26ESect-13.8 P-27ESect-13.8 P-28ESect-13.8 P-29ESect-13.8 P-30ESect-13.8 P-31ESect-13.8 P-32ESect-13.8 P-33ESect-13.8 P-34ESect-13.8 P-35ESect-13.8 P-36ESect-13.8 P-37ESect-13.8 P-38ESect-13.8 P-39ESect-13.8 P-40ESect-13.8 P-41ESect-13.8 P-42ESect-13.8 P-43ESect-13.8 P-44ESect-13.8 P-45ESect-13.8 P-46ESect-13.8 P-47ESect-13.8 P-48ESect-13.8 P-49ESect-13.8 P-50ESect-13.8 P-51ESect-13.8 P-52ESect-13.8 P-53ESect-13.8 P-54ESect-13.8 P-55ESect-13.8 P-56ESect-13.8 P-57ESect-13.8 P-58ESect-13.9 P-1ESect-13.9 P-2ESect-13.9 P-3ESect-13.9 P-4ESect-13.9 P-5ESect-13.9 P-6ESect-13.9 P-7ESect-13.9 P-8ESect-13.9 P-9ESect-13.9 P-10ESect-13.9 P-11ESect-13.9 P-12ESect-13.9 P-13ESect-13.9 P-14ESect-13.9 P-15ESect-13.9 P-16ESect-13.9 P-17ESect-13.9 P-18ESect-13.9 P-19ESect-13.9 P-20ESect-13.9 P-21ESect-13.9 P-22ESect-13.9 P-23ESect-13.9 P-24ESect-13.9 P-25ESect-13.9 P-26ESect-13.9 P-27ESect-13.9 P-28ESect-13.9 P-29ESect-13.9 P-30ESect-13.9 P-31ESect-13.9 P-32ESect-13.9 P-33ESect-13.9 P-34ESect-13.9 P-35ESect-13.9 P-36ESect-13.9 P-37ESect-13.9 P-38ESect-13.9 P-39ESect-13.9 P-40ESect-13.9 P-41ESect-13.10 P-1ESect-13.10 P-2ESect-13.10 P-3ESect-13.10 P-4ESect-13.10 P-5ESect-13.10 P-6ESect-13.10 P-7ESect-13.10 P-8ESect-13.10 P-9ESect-13.10 P-10ESect-13.10 P-11ESect-13.10 P-12ESect-13.10 P-13ESect-13.10 P-14ESect-13.10 P-15ESect-13.10 P-16ESect-13.10 P-17ESect-13.10 P-18ESect-13.10 P-19ESect-13.10 P-20ESect-13.10 P-21ESect-13.10 P-22ESect-13.10 P-23ESect-13.10 P-24ESect-13.10 P-25ESect-13.10 P-26ESect-13.10 P-27ESect-13.10 P-28ESect-13.10 P-29ESect-13.10 P-30ESect-13.10 P-31ESect-13.10 P-32ESect-13.10 P-33ESect-13.10 P-34ESect-13.10 P-35ESect-13.10 P-36ESect-13.10 P-37ESect-13.10 P-38ESect-13.10 P-39ESect-13.10 P-40ESect-13.10 P-41ESect-13.10 P-42ESect-13.10 P-43ESect-13.10 P-44ESect-13.10 P-45ESect-13.10 P-46ESect-13.10 P-47ESect-13.10 P-48ESect-13.10 P-49ESect-13.10 P-50ESect-13.10 P-51ESect-13.10 P-52ESect-13.10 P-53ECh-13 P-1RECh-13 P-2RECh-13 P-3RECh-13 P-4RECh-13 P-5RECh-13 P-6RECh-13 P-7RECh-13 P-8RECh-13 P-9RECh-13 P-10RECh-13 P-11RECh-13 P-12RECh-13 P-13RECh-13 P-14RECh-13 P-15RECh-13 P-16RECh-13 P-17RECh-13 P-18RECh-13 P-19RECh-13 P-20RECh-13 P-21RECh-13 P-22RECh-13 P-23RECh-13 P-24RECh-13 P-25RECh-13 P-26RECh-13 P-27RECh-13 P-28RECh-13 P-29RECh-13 P-30RECh-13 P-31RECh-13 P-32RECh-13 P-33RECh-13 P-34RECh-13 P-35RECh-13 P-36RECh-13 P-37RECh-13 P-38RECh-13 P-39RECh-13 P-40RECh-13 P-41RECh-13 P-42RECh-13 P-43RECh-13 P-44RECh-13 P-45RECh-13 P-46RECh-13 P-47RECh-13 P-48RECh-13 P-49RECh-13 P-50RECh-13 P-51RECh-13 P-52RECh-13 P-53RECh-13 P-54RECh-13 P-55RECh-13 P-56RECh-13 P-57RECh-13 P-58RECh-13 P-59RECh-13 P-60RECh-13 P-61RECh-13 P-62RECh-13 P-63RECh-13 P-64RECh-13 P-65RECh-13 P-66RECh-13 P-67RECh-13 P-68RECh-13 P-69RECh-13 P-70RECh-13 P-71RECh-13 P-72RECh-13 P-73RECh-13 P-74RECh-13 P-75RECh-13 P-76RECh-13 P-77RECh-13 P-78RECh-13 P-79RECh-13 P-80RECh-13 P-81RECh-13 P-82RECh-13 P-83RECh-13 P-84RECh-13 P-85RECh-13 P-86RECh-13 P-87RECh-13 P-88RECh-13 P-89RECh-13 P-90RECh-13 P-91RECh-13 P-92RECh-13 P-93RECh-13 P-94RECh-13 P-95RECh-13 P-96RECh-13 P-97RECh-13 P-98RECh-13 P-99RECh-13 P-1PSCh-13 P-2PSCh-13 P-3PSCh-13 P-4PSCh-13 P-5PSCh-13 P-6PSCh-13 P-7PSCh-13 P-8PSCh-13 P-9PSCh-13 P-10PSCh-13 P-11PSCh-13 P-12PSCh-13 P-13PSCh-13 P-14PSCh-13 P-15PSCh-13 P-16PSCh-13 P-17PSCh-13 P-18PSCh-13 P-19PSCh-13 P-20PSCh-13 P-21PS

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