   Chapter 8.4, Problem 32E ### 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 = x 2 + sin   2 x 4

To determine

To calculate: The simplified derivative of the trigonometric function y=x2+sin2x4 using trigonometric identities.

Explanation

Given Information:

The provided trigonometric function is y=x2+sin2x4.

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

Quotient rule of differentiation:

ddx[a(x)b(x)]=b(x)a(x)a(x)b(x)[b(x)]2

General power rule of differentiation:

ddx[xn]=nxn1

The sum and difference formula of differentiation:

ddx[f(x)+g(x)]=f'(x)+g'(x)

Cosine double angle formula:

cos2θ=2cos2θ1

Calculation:

Consider the provided trigonometric function is,

y=x2+sin2x4

Apply the sum and difference formula of differentiation on the above function.

dydx=ddx[x2]+ddx[sin2x4]

Factor out the real numbers

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