   Chapter 8.4, Problem 39E ### 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 = ln ( sin 2 x )

To determine

To calculate: The simplified derivative of the trigonometric function y=ln(sin2x) using trigonometric identities.

Explanation

Given Information:

The trigonometric function:

y=ln(sin2x)

Formula used:

Logarithmic differentiation rule:

ddx[ln(u)]=1ududx

Sine differentiation rule:

ddx[sinu]=cosududx

General power rule of differentiation:

ddx[xn]=nxn1

The sum and difference formula of differentiation:

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

Reciprocal identity:

cosθsinθ=cotθ

Calculation:

Consider the trigonometric function:

y=ln(sin2x)

Apply the logarithmic formula of differentiation on the above function

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