   Chapter 8.4, Problem 28E ### 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 − x cos x 2

To determine

To calculate: The derivative of the trigonometric function y=excosx2.

Explanation

Given Information:

The provided trigonometric function is y=excosx2.

Formula used:

Cosine differentiation rule:

ddx[cosu]=sinududx

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=excosx2

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

dydx=exddx[cosx2]+cosx2ddx[ex]

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

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