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 3.4, Problem 16E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 16E

The derivative of the given function is dydθ=3ncsc2(nθ) .

Explanation of Solution

Given:

The given function is y=3cot(nθ) .

Calculation:

  y=3cot(nθ)

Apply chain rule.

  df(a)dx=dfdadadx

Let f=cota,a=nθ

  dydθ=3dda(cota)ddθ(nθ)

Use derivative rule.

  ddx(xn)=nxn1 and ddx(cotx)=csc2x

  dydθ=3(csc2a)ndydθ=3ncsc2(a)

Substitute the value of a=nθ .

  dydθ=3ncsc2(nθ)

Hence the derivativeof the given function is dydθ=3ncsc2(nθ) .

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