# 有些式子虽然带着 “f”, 但有可能要看作常数处理

## 二、解析

$$\frac{f^{\prime}(a) (x-a) – f(x) + f(a)}{[f(x) – f(a)] f^{\prime}(a) (x-a)}$$

$$\frac{x \textcolor{springgreen}{f^{\prime}(a)} – \textcolor{springgreen}{a f^{\prime}(a)} – f(x) + \textcolor{springgreen}{f(a)} }{[f(x) – \textcolor{springgreen}{f(a)} ] \textcolor{orangered}{\boldsymbol{\cdot}} \textcolor{springgreen}{f^{\prime}(a)} (x – \textcolor{springgreen}{a})}$$

$$\frac{f^{\prime}(a) – f^{\prime}(x)}{f^{\prime}(x) f^{\prime}(a) (x-a) \textcolor{orangered}{\boldsymbol{+}} [f(x) – f(a)]f^{\prime}(a)} \Rightarrow$$

$$\frac{f^{\prime}(a) – f^{\prime}(x)}{ f^{\prime}(a) [f^{\prime}(x)(x-a) + f(x) – f(a)]}$$

$$\frac{\textcolor{orangered}{\boldsymbol{-}} \frac{f^{\prime}(x) – f^{\prime}(a)}{x-a}}{ f^{\prime}(a) \left[f^{\prime}(x) + \frac{f(x) – f(a)}{x-a} \right]}$$

$$\frac{\textcolor{orangered}{\boldsymbol{-}} f^{\prime \prime}(a)}{f^{\prime}(a) [\textcolor{orangered}{\boldsymbol{f^{\prime}(x)}} + f^{\prime}(a)]} \tag{1}$$

$$\lim_{x \rightarrow a} \textcolor{orangered}{\boldsymbol{f^{\prime}(x)}} = \textcolor{springgreen}{\boldsymbol{f^{\prime}(a)}}$$

$$\frac{\textcolor{orangered}{\boldsymbol{-}} f^{\prime \prime}(a)}{f^{\prime}(a) [\textcolor{springgreen}{\boldsymbol{f^{\prime}(a)}} + f^{\prime}(a)]} = \textcolor{green}{\boldsymbol{\frac{\textcolor{orangered}{\boldsymbol{-}} f^{\prime \prime} (a)}{2f^{\prime 2} (a)}}}$$