1. Derivative of an Exponential

2. Find the derivative of f(x) = 2x.
Using the Definition of Derivative to find the Derivative of an Exponential
Find the derivative of f(x) = 2x.
Use a calculator to numerically evaluate the limit.

3. Approximate Derivatives of Exponentials
Function
Derivative
f(x) = 2x
f(x) = ex
f(x) = 3x
f(x) = 4x
f(x) = ax

4. The Derivative of an Exponential
If f(x) = b x, then
Notice if b = e, then

5. The Derivative of an Exponential
If f(x) = b g(x) and g(x) is differentiable, then
Notice if b = e, then

6. Examples
Find the derivative of each function: