BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable.

17. u = f(x, y), where x = x(r, s, t), y = y(r, s, t)

To determine

To write: The Chain Rule for the function u=f(x,y) , where x=x(r,s,t)andy=y(r,s,t) using tree diagram.

Explanation

The given function, u=f(x,y) is differentiable.

Notice that x=x(r,s,t)andy=y(r,s,t) are the functions of r,sandt .

The tree diagram can be drawn for the given function as shown below in Figure 1.

From Figure 1, obtain the Chain Rule for ur , us and ut as follows.

ur=ux

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

Chapter 14 Solutions

Show all chapter solutions add
Sect-14.1 P-11ESect-14.1 P-12ESect-14.1 P-13ESect-14.1 P-14ESect-14.1 P-15ESect-14.1 P-16ESect-14.1 P-17ESect-14.1 P-18ESect-14.1 P-19ESect-14.1 P-20ESect-14.1 P-21ESect-14.1 P-22ESect-14.1 P-23ESect-14.1 P-24ESect-14.1 P-25ESect-14.1 P-26ESect-14.1 P-27ESect-14.1 P-28ESect-14.1 P-29ESect-14.1 P-30ESect-14.1 P-31ESect-14.1 P-32ESect-14.1 P-33ESect-14.1 P-34ESect-14.1 P-35ESect-14.1 P-36ESect-14.1 P-37ESect-14.1 P-38ESect-14.1 P-39ESect-14.1 P-40ESect-14.1 P-41ESect-14.1 P-42ESect-14.1 P-43ESect-14.1 P-44ESect-14.1 P-45ESect-14.1 P-46ESect-14.1 P-47ESect-14.1 P-48ESect-14.1 P-49ESect-14.1 P-50ESect-14.1 P-51ESect-14.1 P-52ESect-14.1 P-53ESect-14.1 P-54ESect-14.1 P-55ESect-14.1 P-56ESect-14.1 P-57ESect-14.1 P-58ESect-14.1 P-59ESect-14.1 P-60ESect-14.1 P-61ESect-14.1 P-62ESect-14.1 P-63ESect-14.1 P-64ESect-14.1 P-65ESect-14.1 P-66ESect-14.1 P-67ESect-14.1 P-68ESect-14.1 P-69ESect-14.1 P-70ESect-14.1 P-71ESect-14.1 P-72ESect-14.1 P-73ESect-14.1 P-74ESect-14.1 P-75ESect-14.1 P-76ESect-14.1 P-77ESect-14.1 P-78ESect-14.1 P-79ESect-14.1 P-80ESect-14.1 P-81ESect-14.2 P-1ESect-14.2 P-2ESect-14.2 P-3ESect-14.2 P-4ESect-14.2 P-5ESect-14.2 P-6ESect-14.2 P-7ESect-14.2 P-8ESect-14.2 P-9ESect-14.2 P-10ESect-14.2 P-11ESect-14.2 P-12ESect-14.2 P-13ESect-14.2 P-14ESect-14.2 P-15ESect-14.2 P-16ESect-14.2 P-17ESect-14.2 P-18ESect-14.2 P-19ESect-14.2 P-20ESect-14.2 P-21ESect-14.2 P-22ESect-14.2 P-23ESect-14.2 P-24ESect-14.2 P-25ESect-14.2 P-26ESect-14.2 P-27ESect-14.2 P-28ESect-14.2 P-29ESect-14.2 P-30ESect-14.2 P-31ESect-14.2 P-32ESect-14.2 P-33ESect-14.2 P-34ESect-14.2 P-35ESect-14.2 P-36ESect-14.2 P-37ESect-14.2 P-38ESect-14.2 P-39ESect-14.2 P-40ESect-14.2 P-41ESect-14.2 P-42ESect-14.2 P-43ESect-14.2 P-44ESect-14.2 P-45ESect-14.2 P-46ESect-14.3 P-1ESect-14.3 P-2ESect-14.3 P-3ESect-14.3 P-4ESect-14.3 P-5ESect-14.3 P-6ESect-14.3 P-7ESect-14.3 P-8ESect-14.3 P-9ESect-14.3 P-10ESect-14.3 P-11ESect-14.3 P-12ESect-14.3 P-13ESect-14.3 P-14ESect-14.3 P-15ESect-14.3 P-16ESect-14.3 P-17ESect-14.3 P-18ESect-14.3 P-19ESect-14.3 P-20ESect-14.3 P-21ESect-14.3 P-22ESect-14.3 P-23ESect-14.3 P-24ESect-14.3 P-25ESect-14.3 P-26ESect-14.3 P-27ESect-14.3 P-28ESect-14.3 P-29ESect-14.3 P-30ESect-14.3 P-31ESect-14.3 P-32ESect-14.3 P-33ESect-14.3 P-34ESect-14.3 P-35ESect-14.3 P-36ESect-14.3 P-37ESect-14.3 P-38ESect-14.3 P-39ESect-14.3 P-40ESect-14.3 P-41ESect-14.3 P-42ESect-14.3 P-43ESect-14.3 P-44ESect-14.3 P-45ESect-14.3 P-46ESect-14.3 P-47ESect-14.3 P-48ESect-14.3 P-49ESect-14.3 P-50ESect-14.3 P-51ESect-14.3 P-52ESect-14.3 P-53ESect-14.3 P-54ESect-14.3 P-55ESect-14.3 P-56ESect-14.3 P-57ESect-14.3 P-58ESect-14.3 P-59ESect-14.3 P-60ESect-14.3 P-61ESect-14.3 P-62ESect-14.3 P-63ESect-14.3 P-64ESect-14.3 P-65ESect-14.3 P-66ESect-14.3 P-67ESect-14.3 P-68ESect-14.3 P-69ESect-14.3 P-70ESect-14.3 P-71ESect-14.3 P-72ESect-14.3 P-73ESect-14.3 P-74ESect-14.3 P-75ESect-14.3 P-76ESect-14.3 P-77ESect-14.3 P-78ESect-14.3 P-79ESect-14.3 P-80ESect-14.3 P-81ESect-14.3 P-82ESect-14.3 P-83ESect-14.3 P-84ESect-14.3 P-85ESect-14.3 P-86ESect-14.3 P-87ESect-14.3 P-88ESect-14.3 P-89ESect-14.3 P-90ESect-14.3 P-91ESect-14.3 P-92ESect-14.3 P-93ESect-14.3 P-94ESect-14.3 P-95ESect-14.3 P-96ESect-14.3 P-97ESect-14.3 P-98ESect-14.3 P-99ESect-14.3 P-100ESect-14.3 P-101ESect-14.3 P-102ESect-14.3 P-103ESect-14.3 P-104ESect-14.4 P-1ESect-14.4 P-2ESect-14.4 P-3ESect-14.4 P-4ESect-14.4 P-5ESect-14.4 P-6ESect-14.4 P-7ESect-14.4 P-8ESect-14.4 P-11ESect-14.4 P-12ESect-14.4 P-13ESect-14.4 P-14ESect-14.4 P-15ESect-14.4 P-16ESect-14.4 P-17ESect-14.4 P-18ESect-14.4 P-19ESect-14.4 P-20ESect-14.4 P-21ESect-14.4 P-22ESect-14.4 P-23ESect-14.4 P-24ESect-14.4 P-25ESect-14.4 P-26ESect-14.4 P-27ESect-14.4 P-28ESect-14.4 P-29ESect-14.4 P-30ESect-14.4 P-31ESect-14.4 P-32ESect-14.4 P-33ESect-14.4 P-34ESect-14.4 P-35ESect-14.4 P-36ESect-14.4 P-37ESect-14.4 P-38ESect-14.4 P-39ESect-14.4 P-40ESect-14.4 P-41ESect-14.4 P-42ESect-14.4 P-43ESect-14.4 P-44ESect-14.4 P-45ESect-14.4 P-46ESect-14.5 P-1ESect-14.5 P-2ESect-14.5 P-3ESect-14.5 P-4ESect-14.5 P-5ESect-14.5 P-6ESect-14.5 P-7ESect-14.5 P-8ESect-14.5 P-9ESect-14.5 P-10ESect-14.5 P-11ESect-14.5 P-12ESect-14.5 P-13ESect-14.5 P-14ESect-14.5 P-15ESect-14.5 P-16ESect-14.5 P-17ESect-14.5 P-18ESect-14.5 P-19ESect-14.5 P-20ESect-14.5 P-21ESect-14.5 P-22ESect-14.5 P-23ESect-14.5 P-24ESect-14.5 P-25ESect-14.5 P-26ESect-14.5 P-27ESect-14.5 P-28ESect-14.5 P-29ESect-14.5 P-30ESect-14.5 P-31ESect-14.5 P-32ESect-14.5 P-33ESect-14.5 P-34ESect-14.5 P-35ESect-14.5 P-36ESect-14.5 P-37ESect-14.5 P-38ESect-14.5 P-39ESect-14.5 P-40ESect-14.5 P-41ESect-14.5 P-42ESect-14.5 P-43ESect-14.5 P-44ESect-14.5 P-45ESect-14.5 P-46ESect-14.5 P-47ESect-14.5 P-48ESect-14.5 P-49ESect-14.5 P-50ESect-14.5 P-51ESect-14.5 P-53ESect-14.5 P-55ESect-14.5 P-56ESect-14.5 P-57ESect-14.5 P-58ESect-14.5 P-59ESect-14.6 P-1ESect-14.6 P-2ESect-14.6 P-3ESect-14.6 P-4ESect-14.6 P-5ESect-14.6 P-6ESect-14.6 P-7ESect-14.6 P-8ESect-14.6 P-9ESect-14.6 P-10ESect-14.6 P-11ESect-14.6 P-12ESect-14.6 P-13ESect-14.6 P-14ESect-14.6 P-15ESect-14.6 P-16ESect-14.6 P-17ESect-14.6 P-18ESect-14.6 P-19ESect-14.6 P-20ESect-14.6 P-21ESect-14.6 P-22ESect-14.6 P-23ESect-14.6 P-24ESect-14.6 P-25ESect-14.6 P-26ESect-14.6 P-27ESect-14.6 P-28ESect-14.6 P-29ESect-14.6 P-30ESect-14.6 P-31ESect-14.6 P-32ESect-14.6 P-33ESect-14.6 P-34ESect-14.6 P-35ESect-14.6 P-36ESect-14.6 P-37ESect-14.6 P-38ESect-14.6 P-39ESect-14.6 P-40ESect-14.6 P-41ESect-14.6 P-42ESect-14.6 P-43ESect-14.6 P-44ESect-14.6 P-45ESect-14.6 P-46ESect-14.6 P-47ESect-14.6 P-48ESect-14.6 P-49ESect-14.6 P-50ESect-14.6 P-51ESect-14.6 P-52ESect-14.6 P-53ESect-14.6 P-54ESect-14.6 P-55ESect-14.6 P-56ESect-14.6 P-57ESect-14.6 P-58ESect-14.6 P-59ESect-14.6 P-60ESect-14.6 P-61ESect-14.6 P-62ESect-14.6 P-63ESect-14.6 P-64ESect-14.6 P-65ESect-14.6 P-66ESect-14.6 P-67ESect-14.6 P-68ESect-14.6 P-69ESect-14.6 P-70ESect-14.7 P-1ESect-14.7 P-2ESect-14.7 P-3ESect-14.7 P-4ESect-14.7 P-5ESect-14.7 P-6ESect-14.7 P-7ESect-14.7 P-8ESect-14.7 P-9ESect-14.7 P-10ESect-14.7 P-11ESect-14.7 P-12ESect-14.7 P-13ESect-14.7 P-14ESect-14.7 P-15ESect-14.7 P-16ESect-14.7 P-17ESect-14.7 P-18ESect-14.7 P-19ESect-14.7 P-20ESect-14.7 P-21ESect-14.7 P-22ESect-14.7 P-23ESect-14.7 P-24ESect-14.7 P-25ESect-14.7 P-26ESect-14.7 P-27ESect-14.7 P-28ESect-14.7 P-29ESect-14.7 P-30ESect-14.7 P-31ESect-14.7 P-32ESect-14.7 P-33ESect-14.7 P-34ESect-14.7 P-35ESect-14.7 P-36ESect-14.7 P-37ESect-14.7 P-38ESect-14.7 P-39ESect-14.7 P-40ESect-14.7 P-41ESect-14.7 P-42ESect-14.7 P-43ESect-14.7 P-44ESect-14.7 P-45ESect-14.7 P-46ESect-14.7 P-47ESect-14.7 P-48ESect-14.7 P-49ESect-14.7 P-50ESect-14.7 P-51ESect-14.7 P-52ESect-14.7 P-53ESect-14.7 P-54ESect-14.7 P-55ESect-14.7 P-56ESect-14.7 P-57ESect-14.7 P-58ESect-14.7 P-59ESect-14.7 P-60ESect-14.8 P-1ESect-14.8 P-2ESect-14.8 P-3ESect-14.8 P-4ESect-14.8 P-5ESect-14.8 P-6ESect-14.8 P-7ESect-14.8 P-8ESect-14.8 P-9ESect-14.8 P-10ESect-14.8 P-11ESect-14.8 P-12ESect-14.8 P-13ESect-14.8 P-14ESect-14.8 P-15ESect-14.8 P-16ESect-14.8 P-17ESect-14.8 P-18ESect-14.8 P-19ESect-14.8 P-20ESect-14.8 P-21ESect-14.8 P-22ESect-14.8 P-23ESect-14.8 P-24ESect-14.8 P-25ESect-14.8 P-27ESect-14.8 P-28ESect-14.8 P-29ESect-14.8 P-30ESect-14.8 P-31ESect-14.8 P-32ESect-14.8 P-33ESect-14.8 P-34ESect-14.8 P-35ESect-14.8 P-36ESect-14.8 P-37ESect-14.8 P-38ESect-14.8 P-39ESect-14.8 P-40ESect-14.8 P-41ESect-14.8 P-42ESect-14.8 P-43ESect-14.8 P-44ESect-14.8 P-45ESect-14.8 P-46ESect-14.8 P-49ESect-14.8 P-50ECh-14 P-1RCCCh-14 P-2RCCCh-14 P-3RCCCh-14 P-4RCCCh-14 P-5RCCCh-14 P-6RCCCh-14 P-7RCCCh-14 P-8RCCCh-14 P-9RCCCh-14 P-10RCCCh-14 P-11RCCCh-14 P-12RCCCh-14 P-13RCCCh-14 P-14RCCCh-14 P-15RCCCh-14 P-16RCCCh-14 P-17RCCCh-14 P-18RCCCh-14 P-19RCCCh-14 P-1RQCh-14 P-2RQCh-14 P-3RQCh-14 P-4RQCh-14 P-5RQCh-14 P-6RQCh-14 P-7RQCh-14 P-8RQCh-14 P-9RQCh-14 P-10RQCh-14 P-11RQCh-14 P-12RQCh-14 P-1RECh-14 P-2RECh-14 P-3RECh-14 P-4RECh-14 P-5RECh-14 P-6RECh-14 P-7RECh-14 P-8RECh-14 P-9RECh-14 P-10RECh-14 P-11RECh-14 P-12RECh-14 P-13RECh-14 P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Use the guidelines of Section 4.5 to sketch the curve. y = x + ln(x2 + 1)

Single Variable Calculus: Early Transcendentals, Volume I

(916)1/2

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

In Exercises 21 to 32, solve each equation. 3x3=6

Elementary Geometry For College Students, 7e

Evaluate the integral. 21. dt(t21)2

Single Variable Calculus: Early Transcendentals

The graph of x = 2 + 3t, y = 4 − t is a: circle ellipse line parabola

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: is a convergent series.

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