导数定义

$f'(x)= \lim\limits_{\Delta x \to 0} \cfrac{f(x +\Delta x)-f(x)}{\Delta x}$ (⭐)

$f'(a)=\lim\limits_{x\to a} \cfrac{f(x)-f(a)}{x-a}$

微分定义

$\Delta y = A\Delta x + o(\Delta x) \quad (线性主部:A\Delta x = dy = y'_x\Delta x)$

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