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$$$3 u - 4$$$ 的導數
您的輸入
求$$$\frac{d}{du} \left(3 u - 4\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{du} \left(3 u - 4\right)\right)} = {\color{red}\left(\frac{d}{du} \left(3 u\right) - \frac{d}{du} \left(4\right)\right)}$$常數的導數為$$$0$$$：
$$- {\color{red}\left(\frac{d}{du} \left(4\right)\right)} + \frac{d}{du} \left(3 u\right) = - {\color{red}\left(0\right)} + \frac{d}{du} \left(3 u\right)$$套用常數倍法則 $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$，使用 $$$c = 3$$$ 與 $$$f{\left(u \right)} = u$$$：
$${\color{red}\left(\frac{d}{du} \left(3 u\right)\right)} = {\color{red}\left(3 \frac{d}{du} \left(u\right)\right)}$$套用冪次法則 $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{du} \left(u\right) = 1$$$：
$$3 {\color{red}\left(\frac{d}{du} \left(u\right)\right)} = 3 {\color{red}\left(1\right)}$$因此，$$$\frac{d}{du} \left(3 u - 4\right) = 3$$$。
答案
$$$\frac{d}{du} \left(3 u - 4\right) = 3$$$A
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