   Chapter 8.4, Problem 7E ### 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 1-28, find the derivative of the trigonometric function. See Examples 1, 2, 3, y  = sin 2   x

To determine

To calculate: The derivative of the trigonometric function y=sin2x.

Explanation

Given Information:

The provided trigonometric function is y=sin2x.

Formula used:

Cosine differentiation rule:

ddx[cosu]=sinududx

General power rule of differentiation:

ddx[xn]=nxn1

Power reducing formula:

sin2θ=12(1cos2θ)

Calculation:

Consider the provided trigonometric function is,

y=sin2x

Rewrite the above trigonometric function in Cosine trigonometric function using power reducing formula.

y=12(1cos2x)

Now, consider u=2x.

Then, the provided trigonometric function became as,

y=12(1cosu)

Differentiate the above function y with respect to x by using Cosine and general power rule of differentiation

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