Presentation is loading. Please wait.

Presentation is loading. Please wait.

Derivatives of Exponential and Logarithmic Functions

Similar presentations


Presentation on theme: "Derivatives of Exponential and Logarithmic Functions"— Presentation transcript:

1 Derivatives of Exponential and Logarithmic Functions
AP Calculus AB Derivatives of Exponential and Logarithmic Functions

2 Look at the graph of If we assume this to be true, then: The slope at x=0 appears to be 1. definition of derivative

3 Now we attempt to find a general formula for the derivative of using the definition.
This is the slope at x=0, which we have assumed to be 1.

4

5 is its own derivative! If we incorporate the chain rule:

6 Example 1

7 Example 2

8 We can now use this formula to find the derivative of
( and are inverse functions.) (chain rule)

9 ( is a constant.) Incorporating the chain rule:

10 Example 3

11 So far today we have: Now it is relatively easy to find the derivative of

12

13 To find the derivative of a common log function, you could just use the change of base rule for logs: The formula for the derivative of a log of any base other than e is:

14 p

15 Example 4 = 1

16 Example 5 = 1

17 Example 6

18 Example 7 First, take the ln of both sides.

19 Example 7 (cont.)


Download ppt "Derivatives of Exponential and Logarithmic Functions"

Similar presentations


Ads by Google