例
> [!question] 题干 > 求=x^2$的二阶导数
> [!done]- 解 > $ > \begin{aligned} > y&=x^2\\ > dy&=d(x^2)&&两边同时微分\\ > &=2xdx&&根据d(x^a)=ax^{a-1}dx\\ > d(dy)&=d(2xdx)&&两边同时微分\\ > d^2y&=2d(xdx)&&根据高阶微分定义d^2f=d(df)；d(cx)=cd(x)\\ > &=2(xd(dx)+dxdx)&&根据d(xy)=xdy+ydx\\ > &=2(xd^2x+(dx)^2)&&根据高阶微分定义d^2f=d(df)；dxdx=(dx)^2\\ > &=2(dx)^2&&自变量的高阶微分为0，即d^2x=0\\ > \Downarrow{}\\ > \frac{d^2y}{(dx)^2}&=2\\ > \frac{d^2y}{dx^2}&=2&&根据约定俗成的记法dx^2=(dx)^2=dxdx\\ > > \end{aligned} > $