4.3 derivative of exponential functions
TRANSCRIPT
![Page 1: 4.3 derivative of exponential functions](https://reader035.vdocuments.us/reader035/viewer/2022062220/55896041d8b42a52718b46b8/html5/thumbnails/1.jpg)
Derivatives of Exponential Functions
![Page 2: 4.3 derivative of exponential functions](https://reader035.vdocuments.us/reader035/viewer/2022062220/55896041d8b42a52718b46b8/html5/thumbnails/2.jpg)
Natural Exponential Function
If , then
Properties:
xxf ln)( xexf )(1
![Page 3: 4.3 derivative of exponential functions](https://reader035.vdocuments.us/reader035/viewer/2022062220/55896041d8b42a52718b46b8/html5/thumbnails/3.jpg)
Solving Exponential – Natural Log Functions:
Rewrite one as the other with base e
Example: Solve 61ln 2 x
![Page 4: 4.3 derivative of exponential functions](https://reader035.vdocuments.us/reader035/viewer/2022062220/55896041d8b42a52718b46b8/html5/thumbnails/4.jpg)
Example: Find the derivative
2
1
xexf
3.
4.
![Page 5: 4.3 derivative of exponential functions](https://reader035.vdocuments.us/reader035/viewer/2022062220/55896041d8b42a52718b46b8/html5/thumbnails/5.jpg)
Differentiate the following functions:
1.
2.
3.
4.
![Page 6: 4.3 derivative of exponential functions](https://reader035.vdocuments.us/reader035/viewer/2022062220/55896041d8b42a52718b46b8/html5/thumbnails/6.jpg)
Use logarithmic differentiation to find
Solution:
![Page 7: 4.3 derivative of exponential functions](https://reader035.vdocuments.us/reader035/viewer/2022062220/55896041d8b42a52718b46b8/html5/thumbnails/7.jpg)
Let’s Practice!!!Differentiate each of the following:
1.
2.
3.
4.