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# Derivative of a Product of Functions Exercises

### Example 1

Let f(x) = x + 1 and g(x) = x

• Find f ' (x).

### Example 2

Let f(x) = x + 1 and g(x) = x.

• Find g ' (x).

### Example 3

Let f(x) = x + 1 and g(x) = x.

• Find f ' (x) × g ' (x).

### Example 4

Let f(x) = x + 1 and g(x) = x.

• Find (f × g)'(x).

### Example 5

Let f(x) = x + 1 and g(x) = x.

• Must the derivative of the function f × g be equal to the product of f ' and g '?

### Example 6

Find the derivative of the following function.

• f(x) = x sin x

### Example 7

What's the derivative of f(x)?

• f(x) = excos x

### Example 8

What's the derivative of the following function?

• f(x) = x ln x

### Example 9

What's g ' (x) for the following function?

• g(x) = 5xex

### Example 10

What's the derivative of g(x)?

•  g(x) = (logx)(logx)

### Example 11

What's the derivative of g(x)?

• g(x) = 5ex

### Example 12

Find the derivative of the following function.

• h(x) = (x2 + 2x)ln x

### Example 13

What is h ' (x) for the following function?

• h(x) = ln cos x

### Example 14

Find the derivative of h(x).

### Example 15

Find the derivative of j(x).

• j(x) = ln x + cos x

### Example 16

What is the derivative of f(x) = (x2 + 2)(x3 – 4).

• Use the product rule.

### Example 17

What's the derivative of f(x) = (x2 + 2)(x3– 4)?

• Rewrite f by multiplying the factors together, then take the derivative.

### Example 18

• What's the derivative of

f(x) = x2exsin x

thinking of the function as

f(x) = (x2)(exsin x).

### Example 19

Find the derivative of the function

f(x) = x3sin cos x

in two different ways. Give the answer with everything multiplied out (instead of factoring out common factors).

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