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

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Chapter 7.4, Problem 38E
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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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Finding and Evaluating Partial Derivatives In Exercises 33-40, find the first partial derivatives with respect to x, y, and z, and evaluate each at the given point.

w = x y e 9 z 3 ;   ( 2 ,   3 ,   − 1 3 )

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=xye9z3 at point (2,3,−13).

Explanation

Given information:

The provided function is w=xye9z3 and the point is (2,3,−13).

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.

Calculation:

Consider the provided function is,

w=xye9z3

Partially derivative of the function w=xye9z3 with respect to x.

∂w∂x=∂∂x(xye9z3)=ye9z3∂∂x(x)=ye9z3(1)=ye9z3

Substitute (x,y,z)=(2,3,−13) into the function ∂w∂x.

∂w∂x|(2,3,−13)=3e9(−13)3=3⋅e−13

Partially derivative of the function w=xye9z3 with respect to y.

∂w∂y=∂∂y(xye9z3)=xe9z3∂∂y(y)=xe9z3(1)=xe9z3

Substitute (x,y,z)=(2,3,−13) into the function ∂w∂y.

∂w∂y|(2,3,−13)=2⋅e9(−13)3=2⋅e−13

Partially derivative of the function w=xye9z3 with respect to z

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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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Critical Thinking When a distribution is mound-shaped symmetric, what is the general relationship among the val...

Understanding Basic Statistics

Sum of Square (SS), variance and standard deviation

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the limit, if it exists. 19. limx2x+2x3+8

Single Variable Calculus

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. Objectives 2 7a2b9a...

Intermediate Algebra

In Exercises 87 to 90, determine whether the given sets are equal. A=3n+1nWB=3n1nN

Mathematical Excursions (MindTap Course List)

In Problems 35-42, simplify each complex fraction. 40.

Mathematical Applications for the Management, Life, and Social Sciences

Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40-amp ...

Probability and Statistics for Engineering and the Sciences

Solve each equation in Exercises 107120 for x, rounding your answer to four significant digits where necessary....

Finite Mathematics

Find an expression for the function whose graph is the given curve. 56.

Single Variable Calculus: Early Transcendentals

Find the exact value of each of the following. csc(330)

Trigonometry (MindTap Course List)

8. Mary Hall purchased a $45,000 20-year endowment life insurance policy when she was 20 years old. She is now ...

Contemporary Mathematics for Business & Consumers

Use the rules of measurement to divide: 6.28m225m

Elementary Technical Mathematics

Label each of the following statements as either true or false where R represents a commutative ring with unity...

Elements Of Modern Algebra

The Division Property of Inequality requires that we reverse the inequality symbol when dividing by a negative ...

Elementary Geometry For College Students, 7e

Investigation The interval of convergence of the geometric series n=0(x4)n is (4,4). (a) Find the sum of the se...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding an Indefinite Integral In Exercises 19-40, use a table of integrals to find the indefinite integral. xa...

Calculus of a Single Variable

What is the present value of an annuity? Give an example.

Finite Mathematics for the Managerial, Life, and Social Sciences

For a given box, the height measures 4 m. If the length of the rectangular base is 2 m greater than the width o...

Elementary Geometry for College Students

Evaluating a Line Integral of a Vector Field Using Technology In Exercises 35 and 36, use a computer algebra sy...

Multivariable Calculus

Using the Mean Value Theorem for Integrals In Exercises 47-52, find the value(s) of c guaranteed by the Mean Va...

Calculus (MindTap Course List)

Finding an Equation of a Tangent PlaneIn Exercises 6972, find an equation of the tangent plane to the surface a...

Calculus

Find f(x) if f(x)=1x2 and f(2) = 0. a) 1x+12 b) 1x12 c) 3x3+38 d) 3x338

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

True or False: These lines are skew:

Study Guide for Stewart's Multivariable Calculus, 8th

A psychologist determined that the number of sessions required to obtain the trust ofa new patient is either 1,...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Give brief definitions of the terms population and sample.

Introduction To Statistics And Data Analysis

Given the following barrel scale, thimble scale, and vernier scale settings of a 0.0001-inch micrometer, determ...

Mathematics For Machine Technology

Describe how time, event, or individual sampling is done during behavioral observation, and explain why samplin...

Research Methods for the Behavioral Sciences (MindTap Course List)

Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) provides a good barometer...

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

Identify and explain the common threats to external validity and identify threats when they appear in a researc...

Research Methods for the Behavioral Sciences (MindTap Course List)

Find all real solutions of each equation. b+b+8=2

College Algebra (MindTap Course List)

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