About Lesson
3.4 Derivative of Exponential Functions 指数函数的导数
Differentiate the following statement
微分下列各式
1. e – e
Answer :
![Rendered by QuickLaTeX.com 3e^{3x} + 2e^{-2x}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-9651157c6a51a5078569d005a6419040_l3.png)
2.
Answer :
![Rendered by QuickLaTeX.com \frac{1}{2}{\sqrt e}^{{x}}e^{{\sqrt e}^x}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-cf65c2021e094d24e8890909d03cadeb_l3.png)
3. ![Rendered by QuickLaTeX.com {\sqrt2}^x](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-d110e46c5cd3304b14d5a679c17e0af2_l3.png)
![Rendered by QuickLaTeX.com {\sqrt2}^x](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-d110e46c5cd3304b14d5a679c17e0af2_l3.png)
Answer :
![Rendered by QuickLaTeX.com \frac{1}{2}2^{\frac{1}{2}x}ln2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-cb6686676b4bf361b239575ac43f5898_l3.png)
4. ![Rendered by QuickLaTeX.com 5^{x tan x}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0c5dc97e5366cc95971b7ca9e381d8db_l3.png)
![Rendered by QuickLaTeX.com 5^{x tan x}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0c5dc97e5366cc95971b7ca9e381d8db_l3.png)
Answer :
![Rendered by QuickLaTeX.com (tan x + xsec^{2}x)5^{xtan x}ln5](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c68598f3a5062922c076feab6c9463b6_l3.png)
5. ![Rendered by QuickLaTeX.com e^{{tan}^{-1}{x}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c27640cea2d274b0896e3fb80e227018_l3.png)
![Rendered by QuickLaTeX.com e^{{tan}^{-1}{x}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c27640cea2d274b0896e3fb80e227018_l3.png)
Answer :
6. ![Rendered by QuickLaTeX.com sin^{-1}(e^x)](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7fc656347a05988e62d0ca1cfe93ef9d_l3.png)
![Rendered by QuickLaTeX.com sin^{-1}(e^x)](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7fc656347a05988e62d0ca1cfe93ef9d_l3.png)
Answer :
![Rendered by QuickLaTeX.com \frac{e^x}{\sqrt{1-e^{2x}}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-065c8224bafd1af6ec97f56b46230fbd_l3.png)