   Chapter 8.4, Problem 30E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### 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]=nxn1

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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