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 17E
To determine

Give the proof of the given expression.

Expert Solution

Explanation of Solution

Given:

The given expressionis ddx(cotx)=csc2x .

Calculation:

From left hand side

  ddx(cotx)=ddx(cosxsinx)

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

  ddx(cosxsinx)=sinxddx(cosx)cosxddx(sinx)sin2x

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

  ddx(cosxsinx)=sinx(sinx)cosxcosxsin2xddx(cosxsinx)=sin2xcos2xsin2xddx(cosxsinx)=(sin2x+cos2x)sin2xddx(cosxsinx)=1sin2xddx(cosxsinx)=csc2x=R.H.S

Hence ddx(cotx)=csc2x proved.

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