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 7E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 7E

The derivative of the given function is F'(x)=5(x4+3x22)4(4x3+6x) .

Explanation of Solution

Given:

The given function is F(x)=(x4+3x22)5 .

Calculation:

Use quotient rule.

  F(x)=(x4+3x22)5

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a5,a=x4+3x22

  ddxF(x)=dda(a5)ddx(x4+3x22)

Use power rule.

  ddx(xn)=nxn1

  F'(x)=5a4(4x3+6x0)

Substitute the value of a=x4+3x22 .

  F'(x)=5(x4+3x22)4(4x3+6x)

Hence the derivativeof the given function is F'(x)=5(x4+3x22)4(4x3+6x) .

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