# Exponential Functions 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)