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$$$x y$$$ 关于 $$$x$$$ 的导数
您的输入
求$$$\frac{d}{dx} \left(x y\right)$$$。
解答
对 $$$c = y$$$ 和 $$$f{\left(x \right)} = x$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(x y\right)\right)} = {\color{red}\left(y \frac{d}{dx} \left(x\right)\right)}$$应用幂法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{dx} \left(x\right) = 1$$$：
$$y {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = y {\color{red}\left(1\right)}$$因此，$$$\frac{d}{dx} \left(x y\right) = y$$$。
答案
$$$\frac{d}{dx} \left(x y\right) = y$$$A
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