   Chapter 8.4, Problem 27E ### 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 = e 2 x sin 2 x

To determine

To calculate: The derivative of the trigonometric function y=e2xsin2x.

Explanation

Given Information:

The provided trigonometric function is y=e2xsin2x.

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

Product rule of differentiation:

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

Exponential rule of differentiation:

ddx[eu]=eududx

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided trigonometric function is,

y=e2xsin2x

Apply the product rule of differentiation to find the derivative of the above function.

dydx=e2xddx[sin2x]+sin2xddx[e2x]

Differentiate the above function using general power rule, sine and exponential differentiation rule

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