Exponential Functions: (lesson 1 of 3)

## Exponential Functions - Introductions

If and
,
then the exponential function with base
is given by
.

### Natural Exponential Functions

1. The irrational number
or
.

2. For each real
,
.

3.
is a natural exponential function.

### Derivatives of Exponential Functions

1..

2..

### The hyperbolic cosine and sine functions

The hyperbolic cosine function is defined as

,

while the hyperbolic sine function is defined as

.

### Properties of hyperbolic cosine and sine functions

1.
.

2.
.

3.