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Computing Derivatives

Computing Derivatives

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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