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 8E
To determine

Find the differentiate form of the given function.

Expert Solution

Answer to Problem 8E

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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