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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 2.5, Problem 49E

Textbook Problem

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**Finding Derivatives** In Exercises 41–56, find the derivative of the function. State which differentiation rule(s) you used to find the derivative.

Expert Solution

To determine

**To calculate:** The derivative of the provided function

**Given Information:**

The provided function is

**Formula used:**

Product rule of differentiation:

General power rule of differentiation:

where

Constant rule of differentiation:

where

Simple power rule of differentiation:

where

Constant multiple rule of differentiation:

where

**Calculation:**

Consider the function

Differentiate the function

Apply the property of product rule of differentiation,

Apply the property of general power rule of differentiation,

Calculus: An Applied Approach (MindTap Course List)

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The cost C (In dollars) of...Ch. 2.5 - Credit Card Rate The average annual rate r (in...Ch. 2.6 - Checkpoint 1 Worked-out solution available at...Ch. 2.6 - Checkpoint 2 Worked-out solution available at...Ch. 2.6 - Checkpoint 3 Worked-out solution available at...Ch. 2.6 - Checkpoint 4 Worked-out solution available at...Ch. 2.6 - Checkpoint 5 Worked-out solution available at...Ch. 2.6 - Checkpoint 6 Worked-out solution available at...Ch. 2.6 - In Exercises 1-4, solve the equation. 16t2+292=0Ch. 2.6 - In Exercises 1-4, solve the equation. 16t2+88t=0Ch. 2.6 - In Exercises 1-4, solve the equation....Ch. 2.6 - In Exercises 1-4, solve the equation....Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x2(2x+7)Ch. 2.6 - In Exercises 5-8, find dy/dx. y=(x2+3x)(2x25)Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x22x+7Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x2+3x2x25Ch. 2.6 - In Exercises 9 and 10, find the domain and range...Ch. 2.6 - In Exercises 9 and 10, find the domain and range...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Velocity and Acceleration A ball is propelled...Ch. 2.6 - Velocity and Acceleration A brick becomes...Ch. 2.6 - Velocity and Acceleration The velocity v (in feet...Ch. 2.6 - Stopping Distance A car is traveling at a rate of...Ch. 2.6 - Derivatives of Polynomial Functions Consider the...Ch. 2.6 - HOW DO YOU SEE IT? The graph shows the position,...Ch. 2.6 - Modeling Data The table shows the sales y (in...Ch. 2.6 - Finding a Pattern Develop a general rule for...Ch. 2.6 - True or False? In Exercises 43 and 44, determine...Ch. 2.6 - True or False? In Exercises 43 and 44, determine...Ch. 2.6 - Project: Cell Phone Subscribers in U.S. For a...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 4 Worked-out solution available at...Ch. 2.7 - Checkpoint 5 Worked-out solution available at...Ch. 2.7 - Checkpoint 4 Worked-out solution available at...Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.7 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Production Let x represent the units of labor and...Ch. 2.7 - HOW DO YOU SEE IT? The graph shows the demand...Ch. 2.7 - Health: U.S. Chickenpox Decline The numbers (in...Ch. 2.8 - Checkpoint 1 Worked-out solution available at...Ch. 2.8 - Checkpoint 2 Worked-out solution available at...Ch. 2.8 - Checkpoint 3 Worked-out solution available at...Ch. 2.8 - Checkpoint 4 Worked-out solution available at...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Area The radius r of a circle is increasing at a...Ch. 2.8 - Volume The radius r of a sphere is increasing at a...Ch. 2.8 - Area Let A be the area of a circle of radius r...Ch. 2.8 - Volume Let V be the volume of a sphere of radius r...Ch. 2.8 - Volume A spherical balloon is inflated with gas at...Ch. 2.8 - Volume The radius r of a right circular cone is...Ch. 2.8 - Cost, Revenue, and Profit A company that...Ch. 2.8 - Cost, Revenue, and Profit A company that...Ch. 2.8 - Revenue The revenue R from selling x units of a...Ch. 2.8 - Profit The profit P from selling x units of a...Ch. 2.8 - Volume All edges of a cube are expanding at a rate...Ch. 2.8 - Surface Area All edges of a cube are expanding at...Ch. 2.8 - Boating A boat is pulled by a winch on a dock, and...Ch. 2.8 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2.8 - Air traffic Control An airplane flying at an...Ch. 2.8 - Baseball A (square) baseball diamond has sides...Ch. 2.8 - Air Traffic Control An air traffic controller...Ch. 2.8 - Advertising Costs A retail sporting goods store...Ch. 2.8 - Environment An accident at an oil drilling...Ch. 2.8 - Profit A company is increasing the production of a...Ch. 2.8 - Sales The profit for a product is increasing at a...Ch. 2.8 - HOW DO YOU SEE IT? 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In many applications, it is necessary to write expressions in the form, where is a constant and is an integer....

Mathematical Applications for the Management, Life, and Social Sciences

In Exercises 57 to 60, establish a one-to-one correspondence between the sets. {1,3,6, 10}, {1,2,3,4}

Mathematical Excursions (MindTap Course List)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. Objectives 2 4x2+xy...

Intermediate Algebra

Find equations of the tangents to the curve x = 3t2 + 1, y = 2t3 + 1 that pass through the point (4, 3).

Single Variable Calculus: Early Transcendentals

Change 18 m2 to cm2.

Elementary Technical Mathematics

In Exercises 9 to 28, use the drawings as needed to answer the following questions. Suppose that points A, R, a...

Elementary Geometry For College Students, 7e

Show that each of the following statements is an identity by transforming the left side of each one into the ri...

Trigonometry (MindTap Course List)

Show that the ideal is a maximal ideal of .

Elements Of Modern Algebra

Calculate the total cost, proceeds, and gain (or loss) for the following stock market transactions.
Commissions...

Contemporary Mathematics for Business & Consumers

Deriving an Inequality Given ex1 for x0, it follows that 0xetdt0x1dt Perform this integration to derive the ine...

Calculus of a Single Variable

Finding a Directional Derivative In Exercises 7-10, use Theorem 13.9 to find the directional derivative of the ...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 110, determine whether the equation defines y as a linear function of x. If so, write it in the fo...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 23 to 28, find the equation realtionship requested. Then eliminate fractions and square root radic...

Elementary Geometry for College Students

Evaluate ∫16t3 ln t dt.
4t4 + C
4t3 ln t − 16t3 + C
4t4 − t3 ln t + C
4t4 ln t − t4 + C

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

Finding Volume In Exercises 17-20, use a double integral to find the volume of the indicated solid.

Calculus

Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate cFdr. F(x,y)=xi+yjC:r(t)=(3t+1)i+tj,0...

Multivariable Calculus

Finding Partial Derivatives In Exercises 41-44, use the limit definition of partial derivatives to find fx(x,y)...

Calculus (MindTap Course List)

True or False:
The function f is continuous at (0, 0), where

Study Guide for Stewart's Multivariable Calculus, 8th

Solve each of the following equations using the addition principle of equality. Check each answer. 47=R36

Mathematics For Machine Technology

Write without absolute value symbols. 5+12i

College Algebra (MindTap Course List)

Describe the purpose and responsibilities of the Institutional Review Board (IRB).

Research Methods for the Behavioral Sciences (MindTap Course List)

Two shipping services offer overnight delivery of parcels, and both promise delivery before 10 A.M. A mail-orde...

Introduction To Statistics And Data Analysis

Students in grades 3 through 8 in New York State are required to take a state mathematics exam. To meet the sta...

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

Simple random sampling was used to obtain a sample of n = 100 elements from a population of N = 1000. The sampl...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe in your own words the criteria that the IRB uses to evaluate proposed research.

Research Methods for the Behavioral Sciences (MindTap Course List)

Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, b...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

In Problems 324 fill in the blanks or answer true or false. 10. L{e3tsin2t} = _____

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

When necessary, round off answers to two decimal places. In Exercises1-6, find a the volume and b the surface a...

Mathematics: A Practical Odyssey

Which of the following sets are equal? A={0,1,2}B={xR1x3}C={xR1x3}D={xZ1x3}E={xZ1x3}

Discrete Mathematics With Applications

Americans Using Facebook and LinkedIn. A 2018 Pew Research Center survey (Pew Research website) examined the us...

Essentials Of Statistics For Business & Economics

The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket (Bureau of ...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)