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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)