$$$1 - \frac{1}{x}$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(1 - \frac{1}{x}\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dx} \left(1 - \frac{1}{x}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(1\right) - \frac{d}{dx} \left(\frac{1}{x}\right)\right)}$$常數的導數為$$$0$$$：
$${\color{red}\left(\frac{d}{dx} \left(1\right)\right)} - \frac{d}{dx} \left(\frac{1}{x}\right) = {\color{red}\left(0\right)} - \frac{d}{dx} \left(\frac{1}{x}\right)$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = -1$$$：
$$- {\color{red}\left(\frac{d}{dx} \left(\frac{1}{x}\right)\right)} = - {\color{red}\left(- \frac{1}{x^{2}}\right)}$$因此，$$$\frac{d}{dx} \left(1 - \frac{1}{x}\right) = \frac{1}{x^{2}}$$$。
答案
$$$\frac{d}{dx} \left(1 - \frac{1}{x}\right) = \frac{1}{x^{2}}$$$A
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