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$$$x^{8} - 33$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(x^{8} - 33\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dx} \left(x^{8} - 33\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x^{8}\right) - \frac{d}{dx} \left(33\right)\right)}$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 8$$$：
$${\color{red}\left(\frac{d}{dx} \left(x^{8}\right)\right)} - \frac{d}{dx} \left(33\right) = {\color{red}\left(8 x^{7}\right)} - \frac{d}{dx} \left(33\right)$$常數的導數為$$$0$$$：
$$8 x^{7} - {\color{red}\left(\frac{d}{dx} \left(33\right)\right)} = 8 x^{7} - {\color{red}\left(0\right)}$$因此，$$$\frac{d}{dx} \left(x^{8} - 33\right) = 8 x^{7}$$$。
答案
$$$\frac{d}{dx} \left(x^{8} - 33\right) = 8 x^{7}$$$A
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