# 对等式等号两边同时做操作的时候要注意“对等原则”

## 二、正文

\begin{aligned} & y = x + 1 \\ \Rightarrow \ & \textcolor{orangered}{2} \times y = \textcolor{orangered}{2} \times (x + 1) \\ \\ & y = x + 1 \\ \Rightarrow \ & \textcolor{orangered}{2} \times y = \textcolor{orangered}{2} \times x + \textcolor{orangered}{2} \times 1 \end{aligned}

\begin{aligned} & 2 = 1 + 1 \\ \\ \Rightarrow \ & \frac{\textcolor{orangered}{1}}{2} = \frac{\textcolor{orangered}{1}}{1} + \frac{\textcolor{orangered}{1}}{1} \\ \\ \Rightarrow \ & \textcolor{yellow}{ \frac{1}{2} = 1 + 1 } \end{aligned}

\begin{aligned} & 2 = 1 + 1 \\ \\ \Rightarrow \ & \frac{\textcolor{orangered}{1}}{2} = \frac{\textcolor{orangered}{1}}{1 + 1} \\ \\ \Rightarrow \ & \textcolor{springgreen}{ \frac{1}{2} = \frac{1}{2} } \end{aligned}

\begin{aligned} & y = x^{2} + x \\ \Rightarrow \ & \textcolor{yellow}{ \textcolor{orangered}{\ln} y = \textcolor{orangered}{\ln} x^{2} + \textcolor{orangered}{\ln} x } \\ \Rightarrow \ & \ln y = \ln (x^{2} \cdot x) \\ \end{aligned}

\begin{aligned} & y = x^{2} + x \\ \Rightarrow \ & \textcolor{springgreen}{ \textcolor{orangered}{\ln} y = \textcolor{orangered}{\ln} (x^{2} + x) } \end{aligned}

\begin{aligned} & y = \frac{2}{x} \\ \\ \Rightarrow \ & \textcolor{springgreen}{\boldsymbol{ y ^{\prime} = \frac{-2}{x^{2}} }} \end{aligned}

\begin{aligned} & y = \frac{2}{x} \\ \\ \Rightarrow \ & y ^{\prime} = \frac{2 ^{\prime} }{x ^{\prime}} \\ \\ \Rightarrow \ & \textcolor{yellow}{ y ^{\prime} = \frac{0}{1} = 0 } \end{aligned}

\begin{aligned} & y = x^{x} \\ \Rightarrow \ & y = \mathrm{e}^{\ln x^{x}} \\ \Rightarrow \ & \textcolor{springgreen}{y = \mathrm{e}^{x \ln x}} \end{aligned}

\begin{aligned} & y = x^{x} \\ \Rightarrow \ & \textcolor{pink}{ \mathrm{e}^{\ln y} = e^{\ln x^{x}} } \end{aligned}