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$$$\frac{1}{4 x}$$$的导数
您的输入
求$$$\frac{d}{dx} \left(\frac{1}{4 x}\right)$$$。
解答
对 $$$c = \frac{1}{4}$$$ 和 $$$f{\left(x \right)} = \frac{1}{x}$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(\frac{1}{4 x}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dx} \left(\frac{1}{x}\right)}{4}\right)}$$应用幂次法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，其中 $$$n = -1$$$:
$$\frac{{\color{red}\left(\frac{d}{dx} \left(\frac{1}{x}\right)\right)}}{4} = \frac{{\color{red}\left(- \frac{1}{x^{2}}\right)}}{4}$$因此，$$$\frac{d}{dx} \left(\frac{1}{4 x}\right) = - \frac{1}{4 x^{2}}$$$。
答案
$$$\frac{d}{dx} \left(\frac{1}{4 x}\right) = - \frac{1}{4 x^{2}}$$$A
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