   Chapter 8.4, Problem 63E ### 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 = x   sin   x

To determine

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

Explanation

Given Information:

The trigonometric function:

y=xsinx

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

Cosine differentiation rule:

ddx[cosu]=sinududx

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=xsinx

Apply the product rule, general power rule, and sine rule of differentiation

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