MathJax Render Test

测试数学公式的渲染:

常数和基本初等函数的导数公式

\( ( C)’ = 0 \) \( ( x^\mu)’ = \mu x^{\mu -1 } \) \( ( \sin x)’ = \cos x \) \( ( \cos x)’ = -\sin x \)
\( ( \tan x)’ = \sec^2 x \) \( ( \cot x)’ = -\csc^2 x \) \( ( \sec x)’ = \sec x \tan x \) \( ( \csc x)’ = - \csc x \cot x \)
\( ( a^x)’ = a^x \ln a \) \( ( e^x)’ = e^x \) \( ( \log_a x)’ = \frac{1}{x\ln a} \) \( ( \ln x)’ = \frac{1}{x} \)
\( ( \arcsin x)’ = \frac{1}{\sqrt{1-x^2}} \) \( ( \arccos x)’ == - \frac{1}{\sqrt{1-x^2}} \) \( ( \arctan x)’ = \frac{1}{1+x^2} \) \( ( \mathrm{arccot}, x )’ = - \frac{1}{1+x^2} \)

函数的和、差、积、商的求导法则

\( ( u\pm v)’ = u’ \pm v’ \) \( ( Cu)’ = Cu’ \)
\( ( uv)’ = u’v + uv’ \) \( ( \frac{u}{v})’ = \frac{u’v-uv’}{v^2} \)

反函数的求导法则

$$ [ f^{-1}(x)]’ = \frac{1}{f’(y)} $$

复合函数的求导法则

$$ y’(x) = f’(u) \cdot g’(x) $$