The
displays below shows how the derivative of the exponential function
e^x is found by using "differentiation from first
principles". This version uses the \delta y, \delta x
method, where \delta y means "a small increase in y"
and \delta x means "a small increase in
x".

## Summary/Background

The above display
makes use of an important factor about the exponential function, namely that,
as \delta x \to 0 so \displaystyle
\frac{e^{\delta x} - 1}{\delta x} \to 1 .

## Software/Applets used on this page

## Glossary

### derivative

rate of change, dy/dx, f'(x), , Dx.

### exponential function

A function having variables as exponents.

### function

A rule that connects one value in one set with one and only one value in another set.

### union

The union of two sets A and B is the set containing all the elements of A and B.