# 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 11E
To determine

## Find the differentiate form of the given function.

Expert Solution

The differentiate form of the given function is f'(θ)=secθtanθ(1+secθ)2 .

### Explanation of Solution

Given:

The given function is f(θ)=secθ1+secθ .

Calculation:

Use quotient rule.

(fg)'=gf'fg'g2

f(θ)=secθ1+secθddθf(θ)=(1+secθ)ddθ(secθ)secθddθ(1+secθ)(1+secθ)2

Use derivative rule ddx(secx)=secxtanx .

f'(θ)=(1+secθ)(secθtanθ)secθ(0+secθtanθ)(1+secθ)2f'(θ)=secθtanθ+sec2θtanθsec2θtanθ(1+secθ)2f'(θ)=secθtanθ(1+secθ)2

Hence the differentiate form of the given function is f'(θ)=secθtanθ(1+secθ)2 .

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