BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

Finding Second Partial Derivatives In Exercises 45-52, find the four second partial derivatives. See Example 6.

z = ( 3 x 4 2 y 3 ) 3

To determine

To calculate: The second partial derivatives for the function z=(3x42y3)3.

Explanation

Given information:

The provided function is z=(3x42y3)3.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

According to Higher-Order Partial Derivatives,

x(fx)=2fx2=fxxy(fy)=2fy2=fyyy(fx)=2fyx=fxyx(fy)=2fxy=fyx

Calculation:

Consider the provided function is,

z=(3x42y3)3

Partially derivative of the function z=(3x42y3)3 with respect to x.

zx=x((3x42y3)3)=3(3x42y3)2x(3x42y3)=3(3x42y3)2(12x3)=36x3(3x42y3)2

Partially derivative of the function z=(3x42y3)3 with respect to y.

zy=y((3x42y3)3)=3(3x42y3)2y(3x42y3)=3(3x42y3)2(6y2)=18y2(3x42y3)2

Again, partially derivative of the function zx=36x3(3x42y3)2 with respect to x.

zxx=x(36x3(3x42y3)2)=36x3x((3x42y3)2)+(3x42y3)2x(36x3)=108x2(3x42y3)+(3x42y3)2(108x2)=108x2(3x42y3)(11x42y3)

Again, partially derivative of the function zx=36x3(3x42y3)2 with respect to y

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 P-14ESect-7.2 P-15ESect-7.2 P-16ESect-7.2 P-17ESect-7.2 P-18ESect-7.2 P-19ESect-7.2 P-20ESect-7.2 P-21ESect-7.2 P-22ESect-7.2 P-23ESect-7.2 P-24ESect-7.2 P-25ESect-7.2 P-26ESect-7.2 P-27ESect-7.2 P-28ESect-7.2 P-35ESect-7.2 P-36ESect-7.2 P-37ESect-7.2 P-38ESect-7.2 P-39ESect-7.2 P-40ESect-7.2 P-41ESect-7.2 P-42ESect-7.2 P-43ESect-7.2 P-44ESect-7.2 P-45ESect-7.2 P-46ESect-7.2 P-47ESect-7.2 P-48ESect-7.2 P-49ESect-7.2 P-50ESect-7.2 P-51ESect-7.3 P-1CPSect-7.3 P-2CPSect-7.3 P-3CPSect-7.3 P-4CPSect-7.3 P-5CPSect-7.3 P-1SWUSect-7.3 P-2SWUSect-7.3 P-3SWUSect-7.3 P-4SWUSect-7.3 P-5SWUSect-7.3 P-6SWUSect-7.3 P-7SWUSect-7.3 P-8SWUSect-7.3 P-9SWUSect-7.3 P-10SWUSect-7.3 P-1ESect-7.3 P-2ESect-7.3 P-3ESect-7.3 P-4ESect-7.3 P-5ESect-7.3 P-6ESect-7.3 P-7ESect-7.3 P-8ESect-7.3 P-9ESect-7.3 P-10ESect-7.3 P-11ESect-7.3 P-12ESect-7.3 P-13ESect-7.3 P-14ESect-7.3 P-15ESect-7.3 P-16ESect-7.3 P-17ESect-7.3 P-18ESect-7.3 P-19ESect-7.3 P-20ESect-7.3 P-21ESect-7.3 P-22ESect-7.3 P-23ESect-7.3 P-24ESect-7.3 P-25ESect-7.3 P-26ESect-7.3 P-27ESect-7.3 P-28ESect-7.3 P-29ESect-7.3 P-30ESect-7.3 P-31ESect-7.3 P-32ESect-7.3 P-33ESect-7.3 P-34ESect-7.3 P-35ESect-7.3 P-36ESect-7.3 P-37ESect-7.3 P-38ESect-7.3 P-39ESect-7.3 P-40ESect-7.3 P-41ESect-7.3 P-42ESect-7.3 P-43ESect-7.3 P-44ESect-7.3 P-45ESect-7.3 P-46ESect-7.3 P-47ESect-7.3 P-48ESect-7.3 P-49ESect-7.3 P-50ESect-7.3 P-51ESect-7.3 P-53ESect-7.3 P-54ESect-7.3 P-55ESect-7.4 P-1CPSect-7.4 P-2CPSect-7.4 P-3CPSect-7.4 P-4CPSect-7.4 P-5CPSect-7.4 P-6CPSect-7.4 P-7CPSect-7.4 P-1SWUSect-7.4 P-2SWUSect-7.4 P-3SWUSect-7.4 P-4SWUSect-7.4 P-5SWUSect-7.4 P-6SWUSect-7.4 P-7SWUSect-7.4 P-8SWUSect-7.4 P-9SWUSect-7.4 P-10SWUSect-7.4 P-1ESect-7.4 P-2ESect-7.4 P-3ESect-7.4 P-4ESect-7.4 P-5ESect-7.4 P-6ESect-7.4 P-7ESect-7.4 P-8ESect-7.4 P-9ESect-7.4 P-10ESect-7.4 P-11ESect-7.4 P-12ESect-7.4 P-13ESect-7.4 P-14ESect-7.4 P-15ESect-7.4 P-16ESect-7.4 P-17ESect-7.4 P-18ESect-7.4 P-19ESect-7.4 P-20ESect-7.4 P-21ESect-7.4 P-22ESect-7.4 P-23ESect-7.4 P-24ESect-7.4 P-25ESect-7.4 P-26ESect-7.4 P-27ESect-7.4 P-28ESect-7.4 P-29ESect-7.4 P-30ESect-7.4 P-31ESect-7.4 P-32ESect-7.4 P-33ESect-7.4 P-34ESect-7.4 P-35ESect-7.4 P-36ESect-7.4 P-37ESect-7.4 P-38ESect-7.4 P-39ESect-7.4 P-40ESect-7.4 P-41ESect-7.4 P-42ESect-7.4 P-43ESect-7.4 P-44ESect-7.4 P-45ESect-7.4 P-46ESect-7.4 P-47ESect-7.4 P-48ESect-7.4 P-49ESect-7.4 P-50ESect-7.4 P-51ESect-7.4 P-52ESect-7.4 P-53ESect-7.4 P-54ESect-7.4 P-55ESect-7.4 P-56ESect-7.4 P-57ESect-7.4 P-58ESect-7.4 P-59ESect-7.4 P-60ESect-7.4 P-61ESect-7.4 P-62ESect-7.4 P-63ESect-7.4 P-64ESect-7.4 P-65ESect-7.4 P-66ESect-7.4 P-67ESect-7.4 P-68ESect-7.4 P-69ESect-7.4 P-71ESect-7.4 P-72ESect-7.4 P-73ESect-7.5 P-1CPSect-7.5 P-2CPSect-7.5 P-3CPSect-7.5 P-4CPSect-7.5 P-5CPSect-7.5 P-1SWUSect-7.5 P-2SWUSect-7.5 P-3SWUSect-7.5 P-4SWUSect-7.5 P-5SWUSect-7.5 P-6SWUSect-7.5 P-7SWUSect-7.5 P-8SWUSect-7.5 P-9SWUSect-7.5 P-10SWUSect-7.5 P-11SWUSect-7.5 P-12SWUSect-7.5 P-13SWUSect-7.5 P-14SWUSect-7.5 P-1ESect-7.5 P-2ESect-7.5 P-3ESect-7.5 P-4ESect-7.5 P-5ESect-7.5 P-6ESect-7.5 P-7ESect-7.5 P-8ESect-7.5 P-9ESect-7.5 P-10ESect-7.5 P-11ESect-7.5 P-12ESect-7.5 P-13ESect-7.5 P-14ESect-7.5 P-15ESect-7.5 P-16ESect-7.5 P-17ESect-7.5 P-18ESect-7.5 P-19ESect-7.5 P-20ESect-7.5 P-21ESect-7.5 P-22ESect-7.5 P-23ESect-7.5 P-24ESect-7.5 P-25ESect-7.5 P-26ESect-7.5 P-27ESect-7.5 P-28ESect-7.5 P-29ESect-7.5 P-30ESect-7.5 P-31ESect-7.5 P-32ESect-7.5 P-33ESect-7.5 P-34ESect-7.5 P-35ESect-7.5 P-36ESect-7.5 P-37ESect-7.5 P-38ESect-7.5 P-39ESect-7.5 P-40ESect-7.5 P-41ESect-7.5 P-42ESect-7.5 P-43ESect-7.5 P-44ESect-7.5 P-45ESect-7.5 P-46ESect-7.5 P-47ESect-7.5 P-48ESect-7.5 P-49ESect-7.5 P-50ESect-7.5 P-51ESect-7.5 P-53ESect-7.5 P-54ESect-7.5 P-55ESect-7.5 P-56ESect-7.5 P-1QYSect-7.5 P-2QYSect-7.5 P-3QYSect-7.5 P-4QYSect-7.5 P-5QYSect-7.5 P-6QYSect-7.5 P-7QYSect-7.5 P-8QYSect-7.5 P-9QYSect-7.5 P-10QYSect-7.5 P-11QYSect-7.5 P-12QYSect-7.5 P-13QYSect-7.5 P-14QYSect-7.5 P-15QYSect-7.5 P-16QYSect-7.5 P-17QYSect-7.5 P-18QYSect-7.5 P-19QYSect-7.5 P-20QYSect-7.5 P-21QYSect-7.5 P-22QYSect-7.5 P-23QYSect-7.5 P-24QYSect-7.5 P-25QYSect-7.5 P-26QYSect-7.6 P-1CPSect-7.6 P-2CPSect-7.6 P-3CPSect-7.6 P-4CPSect-7.6 P-1SWUSect-7.6 P-2SWUSect-7.6 P-3SWUSect-7.6 P-4SWUSect-7.6 P-5SWUSect-7.6 P-6SWUSect-7.6 P-7SWUSect-7.6 P-8SWUSect-7.6 P-9SWUSect-7.6 P-10SWUSect-7.6 P-1ESect-7.6 P-2ESect-7.6 P-3ESect-7.6 P-4ESect-7.6 P-5ESect-7.6 P-6ESect-7.6 P-7ESect-7.6 P-8ESect-7.6 P-9ESect-7.6 P-10ESect-7.6 P-11ESect-7.6 P-12ESect-7.6 P-13ESect-7.6 P-14ESect-7.6 P-15ESect-7.6 P-16ESect-7.6 P-17ESect-7.6 P-18ESect-7.6 P-19ESect-7.6 P-20ESect-7.6 P-21ESect-7.6 P-22ESect-7.6 P-23ESect-7.6 P-24ESect-7.6 P-25ESect-7.6 P-26ESect-7.6 P-27ESect-7.6 P-28ESect-7.6 P-29ESect-7.6 P-30ESect-7.6 P-31ESect-7.6 P-32ESect-7.6 P-33ESect-7.6 P-34ESect-7.6 P-35ESect-7.6 P-36ESect-7.6 P-37ESect-7.6 P-38ESect-7.6 P-39ESect-7.6 P-40ESect-7.6 P-41ESect-7.6 P-42ESect-7.6 P-43ESect-7.6 P-44ESect-7.6 P-45ESect-7.7 P-1CPSect-7.7 P-2CPSect-7.7 P-3CPSect-7.7 P-1SWUSect-7.7 P-2SWUSect-7.7 P-3SWUSect-7.7 P-4SWUSect-7.7 P-5SWUSect-7.7 P-6SWUSect-7.7 P-7SWUSect-7.7 P-8SWUSect-7.7 P-1ESect-7.7 P-2ESect-7.7 P-3ESect-7.7 P-4ESect-7.7 P-5ESect-7.7 P-6ESect-7.7 P-7ESect-7.7 P-8ESect-7.7 P-9ESect-7.7 P-10ESect-7.7 P-11ESect-7.7 P-12ESect-7.7 P-13ESect-7.7 P-14ESect-7.7 P-15ESect-7.7 P-16ESect-7.7 P-17ESect-7.7 P-18ESect-7.7 P-19ESect-7.7 P-20ESect-7.7 P-21ESect-7.7 P-22ESect-7.7 P-23ESect-7.7 P-24ESect-7.7 P-25ESect-7.7 P-26ESect-7.7 P-27ESect-7.7 P-28ESect-7.7 P-29ESect-7.7 P-30ESect-7.8 P-1CPSect-7.8 P-2CPSect-7.8 P-3CPSect-7.8 P-4CPSect-7.8 P-5CPSect-7.8 P-6CPSect-7.8 P-1SWUSect-7.8 P-2SWUSect-7.8 P-3SWUSect-7.8 P-4SWUSect-7.8 P-5SWUSect-7.8 P-6SWUSect-7.8 P-7SWUSect-7.8 P-8SWUSect-7.8 P-9SWUSect-7.8 P-10SWUSect-7.8 P-11SWUSect-7.8 P-12SWUSect-7.8 P-13SWUSect-7.8 P-14SWUSect-7.8 P-15SWUSect-7.8 P-16SWUSect-7.8 P-1ESect-7.8 P-2ESect-7.8 P-3ESect-7.8 P-4ESect-7.8 P-5ESect-7.8 P-6ESect-7.8 P-7ESect-7.8 P-8ESect-7.8 P-9ESect-7.8 P-10ESect-7.8 P-11ESect-7.8 P-12ESect-7.8 P-13ESect-7.8 P-14ESect-7.8 P-15ESect-7.8 P-16ESect-7.8 P-17ESect-7.8 P-18ESect-7.8 P-19ESect-7.8 P-20ESect-7.8 P-21ESect-7.8 P-22ESect-7.8 P-23ESect-7.8 P-24ESect-7.8 P-25ESect-7.8 P-26ESect-7.8 P-27ESect-7.8 P-28ESect-7.8 P-29ESect-7.8 P-30ESect-7.8 P-31ESect-7.8 P-32ESect-7.8 P-33ESect-7.8 P-34ESect-7.8 P-35ESect-7.8 P-36ESect-7.8 P-37ESect-7.8 P-38ESect-7.8 P-39ESect-7.8 P-40ESect-7.8 P-41ESect-7.8 P-42ESect-7.8 P-43ESect-7.8 P-44ESect-7.8 P-45ESect-7.8 P-46ESect-7.8 P-47ESect-7.8 P-48ESect-7.8 P-49ESect-7.8 P-50ESect-7.8 P-51ESect-7.8 P-52ESect-7.8 P-53ESect-7.8 P-54ESect-7.8 P-55ESect-7.8 P-56ESect-7.8 P-57ESect-7.8 P-58ESect-7.8 P-59ESect-7.8 P-60ESect-7.9 P-1CPSect-7.9 P-2CPSect-7.9 P-3CPSect-7.9 P-4CPSect-7.9 P-5CPSect-7.9 P-1SWUSect-7.9 P-2SWUSect-7.9 P-3SWUSect-7.9 P-4SWUSect-7.9 P-5SWUSect-7.9 P-6SWUSect-7.9 P-7SWUSect-7.9 P-8SWUSect-7.9 P-9SWUSect-7.9 P-10SWUSect-7.9 P-1ESect-7.9 P-2ESect-7.9 P-3ESect-7.9 P-4ESect-7.9 P-5ESect-7.9 P-6ESect-7.9 P-7ESect-7.9 P-8ESect-7.9 P-9ESect-7.9 P-10ESect-7.9 P-11ESect-7.9 P-12ESect-7.9 P-13ESect-7.9 P-14ESect-7.9 P-15ESect-7.9 P-16ESect-7.9 P-17ESect-7.9 P-18ESect-7.9 P-19ESect-7.9 P-20ESect-7.9 P-21ESect-7.9 P-22ESect-7.9 P-23ESect-7.9 P-24ESect-7.9 P-25ESect-7.9 P-26ESect-7.9 P-27ESect-7.9 P-28ESect-7.9 P-29ESect-7.9 P-30ESect-7.9 P-31ESect-7.9 P-32ESect-7.9 P-33ESect-7.9 P-34ESect-7.9 P-35ESect-7.9 P-36ECh-7 P-1RECh-7 P-2RECh-7 P-3RECh-7 P-4RECh-7 P-5RECh-7 P-6RECh-7 P-7RECh-7 P-8RECh-7 P-9RECh-7 P-10RECh-7 P-11RECh-7 P-12RECh-7 P-13RECh-7 P-14RECh-7 P-15RECh-7 P-16RECh-7 P-17RECh-7 P-18RECh-7 P-19RECh-7 P-20RECh-7 P-21RECh-7 P-22RECh-7 P-23RECh-7 P-24RECh-7 P-25RECh-7 P-26RECh-7 P-27RECh-7 P-28RECh-7 P-29RECh-7 P-30RECh-7 P-31RECh-7 P-32RECh-7 P-33RECh-7 P-34RECh-7 P-35RECh-7 P-36RECh-7 P-37RECh-7 P-38RECh-7 P-39RECh-7 P-40RECh-7 P-41RECh-7 P-42RECh-7 P-43RECh-7 P-44RECh-7 P-45RECh-7 P-46RECh-7 P-47RECh-7 P-48RECh-7 P-49RECh-7 P-50RECh-7 P-51RECh-7 P-52RECh-7 P-53RECh-7 P-54RECh-7 P-55RECh-7 P-56RECh-7 P-57RECh-7 P-58RECh-7 P-59RECh-7 P-60RECh-7 P-61RECh-7 P-62RECh-7 P-63RECh-7 P-64RECh-7 P-65RECh-7 P-66RECh-7 P-67RECh-7 P-68RECh-7 P-69RECh-7 P-70RECh-7 P-71RECh-7 P-72RECh-7 P-73RECh-7 P-74RECh-7 P-75RECh-7 P-76RECh-7 P-77RECh-7 P-78RECh-7 P-79RECh-7 P-80RECh-7 P-81RECh-7 P-82RECh-7 P-83RECh-7 P-84RECh-7 P-85RECh-7 P-86RECh-7 P-87RECh-7 P-88RECh-7 P-89RECh-7 P-90RECh-7 P-91RECh-7 P-92RECh-7 P-93RECh-7 P-94RECh-7 P-95RECh-7 P-96RECh-7 P-97RECh-7 P-98RECh-7 P-99RECh-7 P-100RECh-7 P-101RECh-7 P-102RECh-7 P-103RECh-7 P-104RECh-7 P-1TYSCh-7 P-2TYSCh-7 P-3TYSCh-7 P-4TYSCh-7 P-5TYSCh-7 P-6TYSCh-7 P-7TYSCh-7 P-8TYSCh-7 P-9TYSCh-7 P-10TYSCh-7 P-11TYSCh-7 P-12TYSCh-7 P-13TYSCh-7 P-14TYSCh-7 P-15TYSCh-7 P-16TYSCh-7 P-17TYSCh-7 P-18TYSCh-7 P-19TYSCh-7 P-20TYSCh-7 P-21TYSCh-7 P-22TYS

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Find the limit. limxexx2

Single Variable Calculus: Early Transcendentals, Volume I

Evaluate the expression sin Exercises 116. (23)2

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 107-120, factor each expression completely. 116. (x + y)2 1

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Which property of real numbers is illustrated in each part of problem 3-6? 4. a) b)

Mathematical Applications for the Management, Life, and Social Sciences

Find the exact area of the 1350 sector shown.

Elementary Geometry For College Students, 7e

The area of the shaded region is given by:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False: Let . Then f(x, y) is a joint probability function.

Study Guide for Stewart's Multivariable Calculus, 8th

Evaluate each expression. k=1106

College Algebra (MindTap Course List)

Summarize the major APA ethical standards concerning the care and use of animals in research.

Research Methods for the Behavioral Sciences (MindTap Course List)