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$$$\frac{x}{\left|{a}\right|}$$$ 對 $$$x$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(\frac{x}{\left|{a}\right|}\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$，使用 $$$c = \frac{1}{\left|{a}\right|}$$$ 與 $$$f{\left(x \right)} = x$$$：
$${\color{red}\left(\frac{d}{dx} \left(\frac{x}{\left|{a}\right|}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dx} \left(x\right)}{\left|{a}\right|}\right)}$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{dx} \left(x\right) = 1$$$：
$$\frac{{\color{red}\left(\frac{d}{dx} \left(x\right)\right)}}{\left|{a}\right|} = \frac{{\color{red}\left(1\right)}}{\left|{a}\right|}$$因此，$$$\frac{d}{dx} \left(\frac{x}{\left|{a}\right|}\right) = \frac{1}{\left|{a}\right|}$$$。
答案
$$$\frac{d}{dx} \left(\frac{x}{\left|{a}\right|}\right) = \frac{1}{\left|{a}\right|}$$$A
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