# 常用数学公式

### 常用数学公式

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 函数 导函数 备注 $$y = c$$ $y^{\prime}=0$ $c$为常数 $y = x^{\alpha}$ $y^{\prime}=\alpha x^{\alpha - 1}$ $\alpha$为实数 $y=a^{x}(a>0, a \neq 1)$ $y^{\prime}=a^{x} \ln a$ $y=e^{x}$ $y^{\prime}=e^{x}$ $y=\log a^{x}(a>0, a \neq 1)$ $y^{\prime}=\frac{1}{x \ln a}$ $y=\ln x$ $y^{\prime}=\frac{1}{x}$ $y=\sin x$ $y^{\prime}=\cos x$ $y=\cos x$ $y^{\prime}=-\sin x$ $y=\tan x$ $y^{\prime}=\frac{1}{\cos ^{2} x}$ $y=\cot x$ $y^{\prime}=-\frac{1}{\sin ^{2} x}$

$\begin{array}{l}{(u(x) \pm v(x))^{\prime}=u^{\prime}(x) \pm v^{\prime}(x)} \\ {(u(x) \cdot v(x))^{\prime}=u^{\prime}(x) v(x)+u(x) v^{\prime}(x)}\\ \left(\frac{u(x)}{v(x)}\right)^{\prime}=\frac{u^{\prime}(x) v(x)-u(x) v^{\prime}(x)}{v^{2}(x)}\end{array}$

$y_{x}^{\prime}= y_{u}^{\prime} \cdot u_{x}^{\prime} = f^{\prime}(u) \cdot \phi^{\prime}(x)$