科普视频
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例1
> [!question] 题干 > 求^2+y^2=C$的导数
> [!done]- 解 > $ > \begin{aligned} > x^2+y^2&=C\\ > d(x^2+y^2)&=dC&&两边同时微分\\ > d(x^2)+d(y^2)&=0\\ > 2xd(x)+2yd(y)&=0\\ > \frac{dy}{dx}&=-\frac{x}{y}\\ > \end{aligned} > $
例2
> [!question] 题干 > 求^2+2xy-y^2=2x$的导数
> [!done]- 解 > $ > \begin{aligned} > x^2+2xy-y^2&=2x\\ > d(x^2+2xy-y^2)&=d(2x)&&两边同时微分\\ > d(x^2)+d(2xy)-d(y^2)&=2dx\\ > 2xd(x)+2(xdy+ydx)-2ydy&=2dx\\ > (x-y)dy&=(1-x-y)dx&&合并同类项\\ > \frac{dy}{dx}&=\frac{1-x-y}{x-y} > \end{aligned} > $