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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7.4, Problem 6CP
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Find the second partial derivatives of

f ( x , y ) = 4 x 2 y 2 + 2 x + 4 y 2 .

To determine

To calculate: The second partial derivatives for the function f(x,y)=4x2y2+2x+4y2.

Explanation

Given information:

The provided function is f(x,y)=4x2y2+2x+4y2.

Formula used:

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

According to Higher-Order Partial Derivatives,

∂∂x(∂f∂x)=∂2f∂x2=fxx∂∂y(∂f∂y)=∂2f∂y2=fyy∂∂y(∂f∂x)=∂2f∂y∂x=fxy∂∂x(∂f∂y)=∂2f∂x∂y=fyx

Calculation:

Consider the provided function is,

f(x,y)=4x2y2+2x+4y2

Partially derivative of the function f(x,y)=4x2y2+2x+4y2 with respect to x.

fx(x,y)=∂∂x(4x2y2+2x+4y2)=4y2∂∂x(x2)+2∂∂x(x)+4y2∂∂x(1)=8xy2+2

Partially derivative of the function f(x,y)=4x2y2+2x+4y2 with respect to y.

fy(x,y)=∂∂y(4x2y2+2x+4y2)=4x2∂∂y(y2)+2x∂∂y(1)+4∂∂y(y2)=8x2y+8y

Again, partially derivative of the function fx(x,y)=8xy2+2 with respect to x

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
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 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Calculus (MindTap Course List)

In Exercises 49-62, find the indicated limit, if it exists. 56. limx2x+2x2

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

Find the t values that form the boundaries of the critical region for a two-tailed test with =.05 for each of t...

Statistics for The Behavioral Sciences (MindTap Course List)

For Problems 15-20, use the specified number of classes to do the following. (a) Find the class width. (b) Make...

Understanding Basic Statistics

Use the definition of continuity and the properties of limits to show that the function is continuous at the gi...

Single Variable Calculus

In Exercises 25 to 36, determine whether each statement is true or false. If the statement is false, give a rea...

Mathematical Excursions (MindTap Course List)

Rationalize the denominator of xx42 and simplify.

Mathematical Applications for the Management, Life, and Social Sciences

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Finite Mathematics

By how much must the sample size n be increased if the width of the CI (7.5) is to be halved? If the sample siz...

Probability and Statistics for Engineering and the Sciences

For Problems 23-25, answer each question with an algebraic expression. The length of a rectangle is x yards and...

Intermediate Algebra

Use the methods of this section to sketch the curve y = x3 3a2x + 2a3, where a is a positive constant. What do...

Single Variable Calculus: Early Transcendentals

Fill in each blank: 25,000m2=ha

Elementary Technical Mathematics

Use the protractor with measures as indicted to find ABC

Elementary Geometry For College Students, 7e

The current employee tax rate for social security is _____ percent of gross earnings; the current tax rate for ...

Contemporary Mathematics for Business & Consumers

Let B={ bib } be a subset of with the usual operations of addition and multiplication of complex numbers. a. P...

Elements Of Modern Algebra

For each of the following one-to-one functions, find the equation of the inverse. Write the inverse using the n...

Trigonometry (MindTap Course List)

Integration by Tables In Exercises 13 and 14, use a table of integrals with forms involving In u to find the in...

Calculus of a Single Variable

Using Lagrange Multipliers In Exercises 31-38, use Lagrange multipliers to solve the indicated exercise in Sect...

Calculus: Early Transcendental Functions (MindTap Course List)

HOUSING LOANS The chief loan officer of La Crosse Home Mortgage Company summarized the housing loans extended b...

Finite Mathematics for the Managerial, Life, and Social Sciences

Note: Exercises preceded by an asterisk are of a more challenging nature. In Exercises 11 to 22, sketch and des...

Elementary Geometry for College Students

A surface S is parameterized by x = sin u, y = sin v, z = cos v for (u, v) ∈ D, 0 ≤ u ≤ , 0 ≤ v ≤ . A double in...

Study Guide for Stewart's Multivariable Calculus, 8th

Spherical-to-Rectangular Conversion In Exercises 5158, find an equation in rectangular coordinates for the surf...

Calculus

Using a Graph In Exercises 5-10, use graph to estimate the open intervals on which function is increasing or de...

Calculus (MindTap Course List)

Evaluating a Line Integral Using Greens TheoremIn Exercises 1524, use Greens Theorem to evaluate the line integ...

Multivariable Calculus

The best linear fit for the data at the right is y = 3.4 x + 39. An estimate for x = 5 is a) 20 b) 22 c) 24 d) ...

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

Business Schools of Asia-Pacific The pursuit of a higher education degree in business is now international. A s...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Mueller and Oppenheimer (2014) conducted a series of studies comparing the effectiveness of taking classroom no...

Research Methods for the Behavioral Sciences (MindTap Course List)

Practise Solve each problem. Discount An iPad Air is on sale for 413.08. What was the original price of the iPa...

College Algebra (MindTap Course List)

The Lake Placid Town Council has decided to build a new community center to be used for conventions, concerts, ...

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

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal...

Mathematics For Machine Technology

Suppose that 40% of all U.S. employees contribute to a retirement plan (p = 0.40). a. In a random sample of 100...

Introduction To Statistics And Data Analysis

Describe the relationship between the alpha level and the likelihood of making a Type I error.

Research Methods for the Behavioral Sciences (MindTap Course List)

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