反函数的导数

castelu

定理　设$y=f\left( x \right)$为$x = \phi \left( y \right)$的反函数，若$\phi \left( y \right)$在点$y_0$的某邻域内连续，严格单调且$\phi' \left( y \right) \ne 0$，则$f\left( x \right)$在点$x_0 \left( x_0 = \phi \left( y_0 \right) \right)$可导，且
$$f'\left( x_0 \right)=\frac{1}{\phi'\left( y_0 \right)}$$