Derivative of the Natural Number.notebook
April 10, 2015
The Natural Number
The value of e can be determined using limits. Determine...
Value of n
1
2
3
100
1000
100000
10 6
10 8
10 10
We can determine this limit using the Ti83+
Apr 11­1:25 PM
1

Derivative of the Natural Number.notebook
April 10, 2015
Lets try to find the derivative of an exponential function in the form using first principles.
What would make this derivative really easy?
Apr 11­2:29 PM
2

Derivative of the Natural Number.notebook
Can we evaluate this limit?
Try evaluating the limit with various values of b.
> b = 2
> b = 3
April 10, 2015
Apr 11­2:33 PM
3

Derivative of the Natural Number.notebook
April 10, 2015
So can we evaluate
Apr 11­3:17 PM
4

Derivative of the Natural Number.notebook
Derivative of Exponential Functions - Natural Number
If y = e x , then
April 10, 2015
When dealing with a composite function involving e x , then the chain rule is applied. Thus ....
Apr 11­2:56 PM
5

Derivative of the Natural Number.notebook
Lets try some ......
Determine the derivative for each of the following:
April 10, 2015
Apr 11­3:06 PM
6

Derivative of the Natural Number.notebook
April 10, 2015
Apr 11­3:10 PM
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Derivative of the Natural Number.notebook
April 10, 2015
Determine the equation of the tangent line to the curve when x = 2.
Apr 11­3:11 PM
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