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Computing Derivatives Exercises

Example 1

Let f(x) = e^x. 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) = e^x. 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) = e^x. 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) = e^x is its own derivative to find the following value.

f ' (5)

Example 5

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

f ' (-2)

Example 6

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

f ' (ln 5)

Example 7

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

f ' (0)

Example 8

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

Example 9

Let f(x) = 3^x. Find each of the following.

f ' (x)
f ' (2)
f ' (-2)

Example 10

Let g(x) = 5^x. Find each of the following.

g ' (x)
g ' (0)
g ' (0.5)

Example 11

Let h(x) = e^x. Find each of the following.

h ' (x)
h ' (-1)
h ' (5)