# Find the differentiate form of the given function. ### 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 4E
To determine

## Find the differentiate form of the given function.

Expert Solution

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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