   Chapter 8.4, Problem 33E ### 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 = sin 2 x − cos   2 x

To determine

To calculate: The simplified derivative of the trigonometric function y=sin2xcos2x using trigonometric identities.

Explanation

Given Information:

The provided trigonometric function is y=sin2xcos2x.

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

Cosine differentiation rule:

ddx[cosu]=sinududx

General power rule of differentiation:

ddx[xn]=nxn1

The sum and difference formula of differentiation:

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

Sine double angle formula:

sin2θ=2sinθcosθ

Calculation:

Consider the provided trigonometric function is,

y=sin2xcos2x

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

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