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 11E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 11E

The derivative of the given function is f'(z)=2z(z2+1)2 .

Explanation of Solution

Given:

The given function is f(z)=1z2+1 .

Calculation:

  f(z)=1z2+1=(z2+1)1

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a1,a=z2+1

  ddzf(z)=dda(a1)ddz(z2+1)

Use power rule.

  ddx(xn)=nxn1

  f'(z)=1a2(2z)

Substitute the value of a=z2+1 .

  f'(z)=2z(z2+1)2

Hence the derivativeof the given function is f'(z)=2z(z2+1)2 .

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