# Find the differentiate form of the given function.

### 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 8E
To determine

## Find the differentiate form of the given function.

Expert Solution

The differentiate form of the given function is f'(t)=(csc2t+cott)et .

### Explanation of Solution

Given:

The given function is f(t)=cottet .

Calculation:

Use quotient rule.

(fg)'=gf'fg'g2

f(t)=cottetddtf(t)=etddt(cott)cottddt(et)(et)2

Use ddx(cotx)=csc2x and ddx(ex)=ex

f'(t)=et(csc2t)etcotte2tf'(t)=et(csc2tcott)e2tf'(t)=(csc2t+cott)et

Hence the differentiate form of the given function is f'(t)=(csc2t+cott)et .

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