Course Content
第4章:坐标变换
高三数学 | 高级数学
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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}

Answer :
3e^{3x} + 2e^{-2x}

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

Answer :
\frac{1}{2}{\sqrt e}^{{x}}e^{{\sqrt e}^x}
3. {\sqrt2}^x
Answer :
\frac{1}{2}2^{\frac{1}{2}x}ln2
4. 5^{x tan x}
Answer :
(tan x + xsec^{2}x)5^{xtan x}ln5
5. e^{{tan}^{-1}{x}}
Answer :

6. sin^{-1}(e^x)
Answer :
\frac{e^x}{\sqrt{1-e^{2x}}}
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