# Find the derivative of the given function.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### 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

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.

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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