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 16E
To determine

Give the proof of the given expression.

Expert Solution

Explanation of Solution

Given:

The given expressionis ddx(secx)=secxtanx .

Calculation:

From left hand side

  ddx(secx)=ddx(1cosx)

Applyquotientrule (fg)'=gf'fg'g2 .

  ddx(1cosx)=cosxddx(1)1ddx(cosx)cos2x

Use derivative rule ddx(constant)=0 and ddx(cosx)=sinx .

  ddx(1cosx)=cosx01(sinx)cos2xddx(1sinx)=sinxcos2xddx(1sinx)=1cosxsinxcosxddx(1sinx)=secxtanx=R.H.S

Hence ddx(secx)=secxtanx proved.

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