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 4E
To determine

Find the differentiate form of the given function.

Expert Solution

Answer to Problem 4E

The differentiate form of the given function is f'(x)=xcosx+sinx2x .

Explanation of Solution

Given:

The given function is f(x)=xsinx .

Calculation:

Use product rule.

  (fg)'=fg'+gf'

  f(x)=xsinxddxf(x)=xddx(sinx)+sinxddx(x)

Use ddx(sinx)=cosx and ddx(x)=12x

  f'(x)=ddx(sinx)+12ddx(cotx)f'(x)=xcosx+sinx12xf'(x)=xcosx+sinx2x

Hence the differentiate form of the given function is f'(x)=xcosx+sinx2x .

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