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 10E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 10E

The derivative of the given function is f'(x)=8x331+x43 .

Explanation of Solution

Given:

The given function is f(x)=(1+x4)23 .

Calculation:

  f(x)=(1+x4)23

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a23,a=1+x4

  ddxf(x)=dda(a23)ddx(1+x4)

Use power rule.

  ddx(xn)=nxn1

  f'(x)=23a3(4x3)

Substitute the value of a=1+x4 .

  f'(x)=8x331+x43

Hence the derivativeof the given function is f'(x)=8x331+x43 .

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