We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Second Derivatives and Beyond

Second Derivatives and Beyond

Third Derivatives and Beyond Exercises

Example 1

Let (x) = x3 + 2.

Find 2(x).

Example 2

Let (x) = x3 + 2.

Find (2)(x).

Example 3

Suppose f (x) is a degree 3 polynomial.

a. What is the degree of '(x)?

b. What is the degree of f (2)(x) ?

c. What is the degree of f (3)(x) ?

Example 4

Suppose f (x) is a degree 9 polynomial.

a. What is the degree of f 8(x) ?

b. What is the degree of f 9(x)?

c. What is the degree of f 10(x)?

Example 5

Suppose f (x) is a degree n polynomial.

a. What is the degree of f (n – 1)(x)?

b. What is the degree of f (n)(x)?

c. What is the degree of f (k)(x) where k is any integer greater than n?

Example 6

Find the first nine derivatives of the function f (x) = sin x.

Example 7

Let f (x) = sin x. Find the derivative.

f (12)(x)

Example 8

Let f (x) = sin x. Find the derivative.

f (22)(x)

Example 9

Let f (x) = sin x. Find the derivative.

f (33)(x)

Example 10

What are some functions that are infinitely differentiable?

Advertisement