# Computing Derivatives

# 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)