# 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 6E
To determine

## Find the differentiate form of the given equation.

Expert Solution

The differentiate form of the given function is g'(θ)=eθ[tan2θ+tanθθ] .

### Explanation of Solution

Given:

The given functionis g(θ)=eθ(tanθθ) .

Calculation:

Use product rule.

(fg)'=fg'+gf'

ddθg(θ)=eθddθ(tanθθ)+(tanθθ)ddθ(eθ)

Use derivative rule

ddx(x)=1,ddx(ex)=ex and ddx(tanx)=sec2x

g'(θ)=eθ[ddθ(tanθ)ddθ(θ)]+(tanθθ)ddθ(eθ)(tanθθ)ddθ(eθ)g'(θ)=eθ[sec2θ1]+(tanθθ)eθg'(θ)=eθ[tan2θ+tanθθ]

Hence the differentiate form of the given equationis g'(θ)=eθ[tan2θ+tanθθ] .

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