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$$$\frac{5}{x}$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(\frac{5}{x}\right)$$$。
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 $$$c = 5$$$ 與 $$$f{\left(x \right)} = \frac{1}{x}$$$：
$${\color{red}\left(\frac{d}{dx} \left(\frac{5}{x}\right)\right)} = {\color{red}\left(5 \frac{d}{dx} \left(\frac{1}{x}\right)\right)}$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = -1$$$：
$$5 {\color{red}\left(\frac{d}{dx} \left(\frac{1}{x}\right)\right)} = 5 {\color{red}\left(- \frac{1}{x^{2}}\right)}$$因此，$$$\frac{d}{dx} \left(\frac{5}{x}\right) = - \frac{5}{x^{2}}$$$。
答案
$$$\frac{d}{dx} \left(\frac{5}{x}\right) = - \frac{5}{x^{2}}$$$A
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