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