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Update 1math.md
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870138612 authored Aug 13, 2024
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- 反函数的导数
- 设$y=f(x)$为单调,可导函数,且$f'(x)\not=0$,则存在反函数$x=\varphi(y)$,且$\frac{dx}{dy}=\frac{1}{\frac{dy}{dx}}$,即$\varphi'=\frac{1}{f'(x)}$.
- 设$y=f(x)$为单调,可导函数,且$f'(x)\not=0$,则存在反函数$x=\varphi(y)$,且$\frac{dx}{dy}=\frac{1}{\frac{dy}{dx}}$,即$\varphi'(y)=\frac{1}{f'(x)}$.
- 记$f'(x)=y'_x$,$\varphi'(y)=x'_y$,则

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