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

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Chapter 8.4, Problem 30E
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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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Differentiating Trigonometric Functions In Exercises 29-40, find the derivative of the function and simplify your answer by using the trigonometric identities listed in Section 8.2.

y = 1 4 sin 2 2 x

To determine

To calculate: The simplified derivative of the trigonometric function y=14sin22x using trigonometric identities.

Explanation

Given Information:

The provided trigonometric function is y=14sin22x.

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

General power rule of differentiation:

ddx[xn]=nxn−1

Double angle formula:

sin2θ=2sinθcosθ

Calculation:

Consider the provided trigonometric function is,

y=14sin22x

Apply the general power rule of differentiation on the above function.

dydx=ddx[14(sin2x)2]=14ddx[(sin2x)2]=24sin2xddx(sin2x)

Now, apply the sine rule of differentiation

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
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Calculus (MindTap Course List)

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Study Guide for Stewart's Multivariable Calculus, 8th

The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5. a. What is the point estim...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Self Check Write the inequality 0x3 in interval notation and graph it.

College Algebra (MindTap Course List)

An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 ...

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

Explain the advantages and disadvantages of using random assignment as a method to prevent individual differenc...

Research Methods for the Behavioral Sciences (MindTap Course List)

Explain the advantages and disadvantages of a stratified random sample compared with a proportionate stratified...

Research Methods for the Behavioral Sciences (MindTap Course List)

Let c1, c2, , ck denote k specified numbers, and consider the quantity defined by =c11+c22++ckk A confidence i...

Introduction To Statistics And Data Analysis

Write the complement of each of the following angles. a. 41 b. 9932' c. 10303'27"

Mathematics For Machine Technology

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