From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
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.

Exponential Functions Exercises

Example 1

Let f(x) = ex. For the value of a, fill in the table and use the resulting values to estimate f ' (a). 

  • a = 0 

Example 2

Let f(x) = ex. For the value of a, fill in the table and use the resulting values to estimate f ' (a).

  • a = 1

Example 3

Let f(x) = ex. For the value of a, fill in the table and use the resulting values to estimate f ' (a).

  • a = 2

Example 4

Use the fact that f(x) = ex is its own derivative to find the following value.

  • f ' (5)

Example 5

Use the fact that f(x) = ex is its own derivative to find the following value. 

  • f ' (-2)

Example 6

Use the fact that f(x) = ex is its own derivative to find the following value. 

  • f ' (ln 5)

Example 7

Use the fact that f(x) = ex is its own derivative to find the following value.

  • f ' (0)

Example 8

Use the fact that f(x) = ex is its own derivative to find the following value.

Example 9

  • Let f(x) = 3x. Find each of the following.
  1. f ' (x)
      
  2. f ' (2)
      
  3. f ' (-2)
      

Example 10

  • Let g(x) = 5x. Find each of the following.
  1. g ' (x)
      
  2. g ' (0)
      
  3. g ' (0.5)
      

Example 11

  • Let h(x) = ex. Find each of the following.
  1. h ' (x)
      
  2. h ' (-1)
      
  3. h ' (5)
      
Advertisement