Chapter 2.6, Problem 3E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

50 views

(a) Find *y′* by implicit differentiation.

(b) Solve the equation explicitly for *y* and differentiate to get *y′* in terms of *x.*

(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for *y* into your solution for part (a).

To determine

**To find:**

y' by using implicit differentiation.

**Solution: **

Explanation

**1) Formula:**

i. Power rule:

ii. Constant rule:

**2) Given:**

**3) Calculation:**

Differentiating the equation

By using power rule and Chain rule for y term,

Solving for dy/dx, subtract entire x term from both side

Divide both sides by

Therefore,

By canceling common factors

Now convert negative exponent to positive by flipping the term from top to bottom and vice versa,

By writing the exponent term to radical,

**Conclusion:**

Therefore,

**(b)**

**To Solve:**

the equation explicitly for y and then differentiate it to get y’

**Solution:**

To solve the given equation

**1) Calculation:**

Squaring both sides,

This can be simplify further by using

Now differentiate above equation with respect to ‘x’

Show all chapter solutions

Sect-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-10E

Sect-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-2.2 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-2.3 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-2.3 P-45ESect-2.3 P-46ESect-2.3 P-47ESect-2.3 P-48ESect-2.3 P-49ESect-2.3 P-50ESect-2.3 P-51ESect-2.3 P-52ESect-2.3 P-53ESect-2.3 P-54ESect-2.3 P-55ESect-2.3 P-56ESect-2.3 P-57ESect-2.3 P-58ESect-2.3 P-59ESect-2.3 P-60ESect-2.3 P-61ESect-2.3 P-62ESect-2.3 P-63ESect-2.3 P-64ESect-2.3 P-65ESect-2.3 P-66ESect-2.3 P-67ESect-2.3 P-68ESect-2.3 P-69ESect-2.3 P-70ESect-2.3 P-71ESect-2.3 P-72ESect-2.3 P-73ESect-2.3 P-74ESect-2.3 P-75ESect-2.3 P-76ESect-2.3 P-77ESect-2.3 P-78ESect-2.3 P-79ESect-2.3 P-80ESect-2.3 P-81ESect-2.3 P-82ESect-2.3 P-83ESect-2.3 P-84ESect-2.3 P-85ESect-2.3 P-86ESect-2.3 P-87ESect-2.3 P-88ESect-2.3 P-89ESect-2.3 P-90ESect-2.3 P-91ESect-2.3 P-92ESect-2.3 P-93ESect-2.3 P-94ESect-2.3 P-95ESect-2.3 P-96ESect-2.3 P-97ESect-2.3 P-98ESect-2.3 P-99ESect-2.3 P-100ESect-2.3 P-101ESect-2.3 P-102ESect-2.3 P-103ESect-2.3 P-104ESect-2.3 P-105ESect-2.3 P-106ESect-2.3 P-107ESect-2.3 P-108ESect-2.3 P-109ESect-2.3 P-110ESect-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-2.5 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-2.5 P-74ESect-2.5 P-75ESect-2.5 P-76ESect-2.5 P-77ESect-2.5 P-78ESect-2.5 P-79ESect-2.5 P-80ESect-2.5 P-81ESect-2.5 P-82ESect-2.5 P-83ESect-2.5 P-84ESect-2.5 P-85ESect-2.5 P-86ESect-2.5 P-87ESect-2.5 P-88ESect-2.5 P-89ESect-2.5 P-90ESect-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-2.6 P-46ESect-2.6 P-47ESect-2.6 P-48ESect-2.6 P-49ESect-2.6 P-50ESect-2.6 P-51ESect-2.6 P-52ESect-2.6 P-53ESect-2.6 P-54ESect-2.6 P-55ESect-2.6 P-56ESect-2.6 P-57ESect-2.6 P-58ESect-2.6 P-59ESect-2.6 P-60ESect-2.6 P-61ESect-2.6 P-62ESect-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-2.8 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-26ESect-2.8 P-27ESect-2.8 P-28ESect-2.8 P-29ESect-2.8 P-30ESect-2.8 P-31ESect-2.8 P-32ESect-2.8 P-33ESect-2.8 P-34ESect-2.8 P-35ESect-2.8 P-36ESect-2.8 P-37ESect-2.8 P-38ESect-2.8 P-39ESect-2.8 P-40ESect-2.8 P-41ESect-2.8 P-42ESect-2.8 P-43ESect-2.8 P-44ESect-2.8 P-45ESect-2.8 P-46ESect-2.8 P-47ESect-2.8 P-48ESect-2.8 P-49ESect-2.8 P-50ESect-2.9 P-1ESect-2.9 P-2ESect-2.9 P-3ESect-2.9 P-4ESect-2.9 P-5ESect-2.9 P-6ESect-2.9 P-7ESect-2.9 P-8ESect-2.9 P-9ESect-2.9 P-10ESect-2.9 P-11ESect-2.9 P-12ESect-2.9 P-13ESect-2.9 P-14ESect-2.9 P-15ESect-2.9 P-16ESect-2.9 P-17ESect-2.9 P-18ESect-2.9 P-19ESect-2.9 P-20ESect-2.9 P-21ESect-2.9 P-22ESect-2.9 P-23ESect-2.9 P-24ESect-2.9 P-25ESect-2.9 P-26ESect-2.9 P-27ESect-2.9 P-28ESect-2.9 P-29ESect-2.9 P-30ESect-2.9 P-31ESect-2.9 P-32ESect-2.9 P-33ESect-2.9 P-34ESect-2.9 P-35ESect-2.9 P-36ESect-2.9 P-37ESect-2.9 P-38ESect-2.9 P-39ESect-2.9 P-40ESect-2.9 P-41ESect-2.9 P-42ESect-2.R P-1CCSect-2.R P-2CCSect-2.R P-3CCSect-2.R P-4CCSect-2.R P-5CCSect-2.R P-6CCSect-2.R P-7CCSect-2.R P-8CCSect-2.R P-9CCSect-2.R P-10CCSect-2.R P-11CCSect-2.R P-12CCSect-2.R P-1TFQSect-2.R P-2TFQSect-2.R P-3TFQSect-2.R P-4TFQSect-2.R P-5TFQSect-2.R P-6TFQSect-2.R P-7TFQSect-2.R P-8TFQSect-2.R P-9TFQSect-2.R P-10TFQSect-2.R P-11TFQSect-2.R P-12TFQSect-2.R P-13TFQSect-2.R P-14TFQSect-2.R P-15TFQSect-2.R P-1ESect-2.R P-2ESect-2.R P-3ESect-2.R P-4ESect-2.R P-5ESect-2.R P-6ESect-2.R P-7ESect-2.R P-8ESect-2.R P-9ESect-2.R P-10ESect-2.R P-11ESect-2.R P-12ESect-2.R P-13ESect-2.R P-14ESect-2.R P-15ESect-2.R P-16ESect-2.R P-17ESect-2.R P-18ESect-2.R P-19ESect-2.R P-20ESect-2.R P-21ESect-2.R P-22ESect-2.R P-23ESect-2.R P-24ESect-2.R P-25ESect-2.R P-26ESect-2.R P-27ESect-2.R P-28ESect-2.R P-29ESect-2.R P-30ESect-2.R P-31ESect-2.R P-32ESect-2.R P-33ESect-2.R P-34ESect-2.R P-35ESect-2.R P-36ESect-2.R P-37ESect-2.R P-38ESect-2.R P-39ESect-2.R P-40ESect-2.R P-41ESect-2.R P-42ESect-2.R P-43ESect-2.R P-44ESect-2.R P-45ESect-2.R P-46ESect-2.R P-47ESect-2.R P-48ESect-2.R P-49ESect-2.R P-50ESect-2.R P-51ESect-2.R P-52ESect-2.R P-53ESect-2.R P-54ESect-2.R P-55ESect-2.R P-56ESect-2.R P-57ESect-2.R P-58ESect-2.R P-59ESect-2.R P-60ESect-2.R P-61ESect-2.R P-62ESect-2.R P-63ESect-2.R P-64ESect-2.R P-65ESect-2.R P-66ESect-2.R P-67ESect-2.R P-68ESect-2.R P-69ESect-2.R P-70ESect-2.R P-71ESect-2.R P-72ESect-2.R P-73ESect-2.R P-74ESect-2.R P-75ESect-2.R P-76ESect-2.R P-77ESect-2.R P-78ESect-2.R P-79ESect-2.R P-80ESect-2.R P-81ESect-2.R P-82ESect-2.R P-83ESect-2.R P-84ESect-2.R P-85ESect-2.R P-86ESect-2.R P-87ESect-2.R P-88ESect-2.R P-89ESect-2.R P-90ESect-2.R P-91ESect-2.R P-92ESect-2.P P-1PSect-2.P P-2PSect-2.P P-3PSect-2.P P-4PSect-2.P P-5PSect-2.P P-6PSect-2.P P-7PSect-2.P P-8PSect-2.P P-9PSect-2.P P-10PSect-2.P P-11PSect-2.P P-12PSect-2.P P-13PSect-2.P P-14PSect-2.P P-15PSect-2.P P-16PSect-2.P P-17PSect-2.P P-18PSect-2.P P-19PSect-2.P P-20PSect-2.P P-21PSect-2.P P-22PSect-2.P P-23PSect-2.P P-24PSect-2.P P-25PSect-2.P P-26PSect-2.P P-27PSect-2.P P-28P

Calculus: Early Transcendentals

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: An Applied Approach (MindTap Course List)

Finite Mathematics and Applied Calculus (MindTap Course List)

Applied Calculus

Multivariable Calculus

Calculus: Early Transcendental Functions

Single Variable Calculus: Early Transcendentals, Volume I

Essentials Of Statistics

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Single Variable Calculus

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

Finite Mathematics

Understanding Basic Statistics

Probability and Statistics for Engineering and the Sciences

Elementary Technical Mathematics

Elementary Geometry For College Students, 7e

Intermediate Algebra

Mathematical Applications for the Management, Life, and Social Sciences

Mathematical Excursions (MindTap Course List)

Calculus of a Single Variable

Single Variable Calculus: Early Transcendentals

Trigonometry (MindTap Course List)

Contemporary Mathematics for Business & Consumers

Elements Of Modern Algebra

Calculus: Early Transcendental Functions (MindTap Course List)

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

Study Guide for Stewart's Multivariable Calculus, 8th

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences

Multivariable Calculus

Calculus (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Statistics for Business & Economics, Revised (MindTap Course List)

College Algebra (MindTap Course List)

Mathematics For Machine Technology

Introduction To Statistics And Data Analysis

Research Methods for the Behavioral Sciences (MindTap Course List)

Research Methods for the Behavioral Sciences (MindTap Course List)

Mathematics: A Practical Odyssey