# Find the given derivativeby the help of pattern that occurs.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.3, Problem 40E
To determine

## Find the given derivativeby the help of pattern that occurs.

Expert Solution

The value of the given derivative d35dx35(xsinx)=35sinxxcosx .

### Explanation of Solution

Given:

The given derivativeis d35dx35(xsinx) .

Calculation:

f(x)=xsinx

f1(x)=ddx(xsinx)=sinx+xcosx(productrule)f2(x)=ddx(sinx+xcosx)=cosx+cosxxsinx=2cosxxsinx(sum and productrule)f3(x)=ddx(2cosxxsinx)=3sinxxcosx(difference and productrule)f4(x)=ddx(3sinxxcosx)=4cosx+xsinx(sum and productrule)f5(x)=ddx(4cosx+xsinx)=5sinx+xcosx(difference and productrule)f6(x)=ddx(5sinx+xcosx)=6cosxxsinx(sum and productrule)f7(x)=ddx(6cosxxsinx)=7sinxxcosx(difference and productrule)f8(x)=ddx(7sinxxcosx)=8cosx+xsinx(sum and productrule)

From the above pattern

f35(x)=35sinxxcosx

Hence thevalue of the given derivative d35dx35(xsinx)=35sinxxcosx .

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