Lesson 3.4 - Deriving Exponential Functions
Exponential functions are any function whose power is the variable and base is a constant.
The derivative ALWAYS follows this form.
Functions of base e have the nice property of having the natural log disappear...
What about taking the derivative of a log?
The rule is to take one over what is being "logged". If the log is not of base e, then the natural log of that base needs to be divided as well.
Now, what is e?
As a number, it is equal to Where does this number come from? It actually has a few definitions:
2) e is the unique positive number for which
The second definition can be easily shown using the definition of a derivative.
Not much further detail can be discussed until the all mighty chain rule is introduced. Stay tuned until the next lesson.