科普视频
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例1
> [!question] 题干 > 求(x,y)=e^{xy^2}$的导数
> [!done]- 解 > $ > \begin{aligned} > > z(x,y)&=e^{xy^2}\\ > dz&=d(e^{xy^2})&&两边微分\\ > &=e^{xy^2}d(xy^2)&&根据d(e^x)=e^xdx\\ > &=e^{xy^2}(y^2dx+xd(y^2))&&根据d(xy)=xdy+ydx\\ > &=y^2e^{xy^2}dx+2xye^{xy^2}dy&&根据d(x^a)=ax^{a-1}dx，并提取公因式\\ > > &\Downarrow{}&&根据dz=\frac{ \partial z }{ \partial x }dx+\frac{ \partial z }{ \partial y }dy的格式对应\\ > > &\begin{cases} > \frac{ \partial z }{ \partial x }=y^2e^{xy^2}\\ > \frac{ \partial z }{ \partial y }=2xye^{xy^2} > \end{cases} > > \end{aligned} > > > $