# Give the proof of the given expression.

### 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 15E
To determine

## Give the proof of the given expression.

Expert Solution

### Explanation of Solution

Given:

The given expressionis ddx(cscx)=cscxcotx .

Calculation:

From left hand side

ddx(cscx)=ddx(1sinx)

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

ddx(1sinx)=sinxddx(1)1ddx(sinx)sin2x

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

ddx(1sinx)=sinx01cosxsin2xddx(1sinx)=cosxsin2xddx(1sinx)=1sinxcosxsinxddx(1sinx)=cscxcotxddx(1sinx)=cscxcotx=R.H.S

Hence ddx(cscx)=cscxcotx proved.

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