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求导:基础练习

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科普视频

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例:公式的熟练运用

> [!question] 题干 > 求=e^{-x^2}$的导数

> [!done]- 解 > $ > \begin{aligned} > y&=e^{-x^2}\\ > dy&=d(e^{-x^2})&&两边同时微分\\ > &=e^{-x^2}d(-x^2)&&根据d(e^x)=e^xdx\\ > &=-e^{-x^2}d(x^2)&&根据d(cx)=cd(x)\\ > &=-e^{-x^2}\cdot2xdx&&根据d(x^a)=ax^{a-1}dx\\ > &=-2e^{-x^2}xdx\\ > \frac{dy}{dx}&=-2e^{-x^2} > \end{aligned} > $