9. Derivatives of Exponential Functions

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Presentation transcript:

9. Derivatives of Exponential Functions Free Powerpoint Templates

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?

Derivative of ex

Example 2 Find dy/dx if

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?

Derivative of bx Where b is a number

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

Example 5 Evaluate the following

Example 6 Find dy/dx for

Example 7 Find y’’ for

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 ?