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 5E
To determine

Find the differentiate form of the given equation.

Expert Solution

Answer to Problem 5E

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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