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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 2.3, Problem 22E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
1 views

Differentiate the function.

D ( t ) = 1 + 16 t 2 ( 4 t ) 3

To determine

To differentiate:  The function Dt=1+16t24t3

Explanation

Concept:

To differentiate given function, we may use rules of differentiation and also may convert radicals into exponent form if necessary.

Formula:

(i) Power rule:  ddxxn=nxn-1

(ii) Rule of exponent: xnxm=xm-n.

(iii) The addition rule, if f  and g are both differentiable,

Then  ddxfx+gx=ddxfx+ddxg(x)

Given:

Dt=1+16t24t3

Calculations:

We have Dt=1+16t24t3

By simplifying and using rule of exponents, Dt can be written as,

Dt=1+16t24t3=1+16t264t3=164t3+16t264t3=t-364+t-14

Differentiating with respect to t,

By using Addition rule of differentiation,

ddxfx+gx=ddxfx+ ddxgx

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Let a=log2,b=log3, and c=log7. In Exercises 2946, use the logarithm identities to express the given quantity in...

Finite Mathematics

Simplify the algebraic expressions in Problems 15-34 by removing parentheses and combining similar terms. Objec...

Intermediate Algebra

In Exercises 15 to 20, describe the line segments as determined, undetermined, or overdetermined. Use the accom...

Elementary Geometry For College Students, 7e

A sample of 14 joint specimens of a particular type gave a sample mean proportional limit stress of 8.48 MPa an...

Probability and Statistics for Engineering and the Sciences

Change 314 to an improper fraction.

Elementary Technical Mathematics

Find the modes of the sets of scores in Problems 9-12. 9. 3, 4, 3, 2, 2, 3, 5, 7, 6, 2, 3

Mathematical Applications for the Management, Life, and Social Sciences

Difference of Sets Another operation that can be defined on sets A and B is the difference of the sets, denoted...

Mathematical Excursions (MindTap Course List)

Writing Functions Write a function of each specified type that has a limit of 4 as x approaches 8. (a) linear(c...

Calculus of a Single Variable

For what values of x is f continuous? f(x)={0ifxisrational1ifxisirrational

Single Variable Calculus: Early Transcendentals

Velocity of an Arrow An arrow is shot with an initial velocity of 48 feet per second at an angle of elevation o...

Trigonometry (MindTap Course List)

From the following information, determine the number of days of each loan. Loan Date Due Date Number of Days 29...

Contemporary Mathematics for Business & Consumers

In Exercises 16, H is a normal subgroup of the group G. Find the order of the quotient group G/H. Write out the...

Elements Of Modern Algebra

Let .For every partition of R, the double Riemann sum for will be largest if, for each subrectangle, we choose...

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Testing for a Conservative Vector FieldIn Exercises2532, determine whether the vector field is conservative. F(...

Calculus: Early Transcendental Functions (MindTap Course List)

Polar coordinates of the point with rectangular coordinates (5, 5) are: (25, 0)

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In Exercises 34-44, use your calculator value of unless otherwise stated. Round answers to two decimal places....

Elementary Geometry for College Students

In Exercise 16, find the point of intersection of the pair of straight lines with the given equations. Round yo...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. coshxxdx

Calculus

Finding a General Solution In Exercises 43-52, use integration to find a general solution of the differential e...

Calculus (MindTap Course List)

Finding the Angle Between Two Vectors In Exercises 1118, find the angle between the vectors (a) in radians and...

Multivariable Calculus

Mathematics For Machine Technology

Describe the appearance of a scatter plot showing the data from a set of scores that produce a Pearson correlat...

Research Methods for the Behavioral Sciences (MindTap Course List)

The article Most Dog Owners Take More Pictures of Their Pet Than Their Spouse (August 22, 2016, news.fastcompan...

Introduction To Statistics And Data Analysis

Carpetland salespersons average 8000 per week in sales. Steve Contois, the firms vicepresident, proposes a comp...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Three different assembly methods have been proposed for a new product. A completely randomized experimental des...

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

Identify the statistical techniques that are appropriate for each nonexperimental, quasi-experimental, and deve...

Research Methods for the Behavioral Sciences (MindTap Course List)

Find the vertex of each parabola. f(x)=x21

College Algebra (MindTap Course List)

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