1. 9. Derivatives of Exponential Functions
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2. Example 1
On your calculator, sketch the graph of ex and on the same set of axes, using NDERIV, sketch d/dx(ex). What do you notice?

3. Derivative of ex

4. Example 2
Find dy/dx if

5. Example 3
On your calculator, sketch the graph of 2x and on the same set of axes, using NDERIV, sketch d/dx(2x). What do you notice?

6. Derivative of bx
Where b is a number

7. Example 4
At what point on the graph of the function does the tangent line have a slope of 2?

8. Example 5
Evaluate the following

9. Example 6
Find dy/dx for

10. Example 7
Find y’’ for

11. Example 8
A glass of cold milk from the refrigerator is left on the counter on a hot summer day. Its temperature (in degrees Fahrenheit) after sitting on the counter for t minutes is
What is the temperature of the refrigerator? How can you tell?
b) What is the temperature of the room? How can you tell?
c) Determine algebraically when the temperature of the milk reaches 55o ?
d) At what rate is the milk warming up when its temperature is 55o ?