# Find the differentiate form of the given equation.

### 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 5E
To determine

## Find the differentiate form of the given equation.

Expert Solution

The differentiate form of the given function is dydθ=sec3θ+secθtan2θ .

### Explanation of Solution

Given:

The given equationis y=secθtanθ .

Calculation:

Use product rule.

(fg)'=fg'+gf'

dydθ=secθddθ(tanθ)+tanθddθ(secθ)

Use derivative of the trigonometric function.

ddx(secx)=secxtanx and ddx(tanx)=sec2x

dydθ=secθsec2θ+tanθsecθtanθdydθ=sec3θ+secθtan2θ

Hence the differentiate form of the given equationis dydθ=sec3θ+secθtan2θ .

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