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$$$x^{6} - 7$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(x^{6} - 7\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dx} \left(x^{6} - 7\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x^{6}\right) - \frac{d}{dx} \left(7\right)\right)}$$常數的導數為$$$0$$$：
$$- {\color{red}\left(\frac{d}{dx} \left(7\right)\right)} + \frac{d}{dx} \left(x^{6}\right) = - {\color{red}\left(0\right)} + \frac{d}{dx} \left(x^{6}\right)$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 6$$$：
$${\color{red}\left(\frac{d}{dx} \left(x^{6}\right)\right)} = {\color{red}\left(6 x^{5}\right)}$$因此，$$$\frac{d}{dx} \left(x^{6} - 7\right) = 6 x^{5}$$$。
答案
$$$\frac{d}{dx} \left(x^{6} - 7\right) = 6 x^{5}$$$A
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