3.4 Derivative of Exponential Functions 指数函数的导数 - 独中课程 | 线上补习

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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 $^{3x}$ – e $^{-2x}$

$3e^{3x} + 2e^{-2x}$

2. $e^{{\sqrt e}^x}$

$\frac{1}{2}{\sqrt e}^{{x}}e^{{\sqrt e}^x}$

3. ${\sqrt2}^x$

$\frac{1}{2}2^{\frac{1}{2}x}ln2$

4. $5^{x tan x}$

$(tan x + xsec^{2}x)5^{xtan x}ln5$

5. $e^{{tan}^{-1}{x}}$

6. $sin^{-1}(e^x)$

$\frac{e^x}{\sqrt{1-e^{2x}}}$

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