# 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 3E
To determine

## Find the differentiate form of the given function.

Expert Solution

The differentiate form of the given function is f'(x)=cosx12csc2x .

### Explanation of Solution

Given:

The given function is f(x)=sinx+12cotx .

Calculation:

Use power rule and derivative of the trigonometric function.

ddx(sinx)=cosx and ddx(cotx)=csc2x

f(x)=sinx+12cotxddxf(x)=ddx(sinx)+12ddx(cotx)f'(x)=cosx+12(csc2x)f'(x)=cosx12csc2x

Hence the differentiate form of the given function is f'(x)=cosx12csc2x .

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