BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 40E

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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