1. Differentiating Exponential Functions
What is the derivative rule for exponential functions?
How are we going to remove that multiplier?
Where else can we find this constant? What does it represent?

2. Now let's look at this numerically ... remember ... mathematics is the science of patterns

3. Symbolically, we're looking for ...
a "magic" number, such that has slope 1 at
Numerically ...
we now have 2 different definitions for the number
= the function whose slope of the tangent line to the graph of
is

4. 2x
d ax = c·ax
dx
But what about exponential functions with other bases ...

5. How are all these values related?

6. Derivatives of Exponential Functions
The Exponential Function
any exponential function
Let's find these derivatives ...

8. Assignment: p.206-207 #1, 7, 9, 13, 15, 19, 21