   Chapter 8.4, Problem 65E ### 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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# Finding Second Derivatives In Exercises 63–66, find the second derivative of the trigonometric function. y = cos   x 2

To determine

To calculate: The second derivative of the trigonometric function y=cosx2.

Explanation

Given Information:

The trigonometric function:

y=cosx2

Formula used:

Cosine differentiation rule:

ddx[cosu]=sinududx

Sine differentiation rule:

ddx[sinu]=cosdudx

Product rule of differentiation:

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

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the trigonometric function:

y=cosx2

Apply the general power rule and cosine rule of differentiation.

y'=ddx[cosx2]=sinx2(2x)=2xsinx2

Now, apply the product rule, general power rule, and sine rule of differentiation on the above function again

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