   Chapter 8.4, Problem 31E ### 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 = cos 2 x − sin 2 x

To determine

To calculate: The simplified derivative of the trigonometric function y=cos2xsin2x using trigonometric identities.

Explanation

Given Information:

The provided trigonometric function is y=cos2xsin2x.

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

Cosine differentiation rule:

ddx[cosu]=sinududx

General power rule of differentiation:

ddx[xn]=nxn1

Double angle formula:

sin2θ=2sinθcosθ

Calculation:

Consider the provided trigonometric function is,

y=cos2xsin2x

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

dydx=ddx[(cosx)2]ddx[

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