BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

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

Answer to Problem 6E

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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