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$$$3 x z$$$ 對 $$$z$$$ 的導數
您的輸入
求$$$\frac{d}{dz} \left(3 x z\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{dz} \left(c f{\left(z \right)}\right) = c \frac{d}{dz} \left(f{\left(z \right)}\right)$$$，使用 $$$c = 3 x$$$ 與 $$$f{\left(z \right)} = z$$$：
$${\color{red}\left(\frac{d}{dz} \left(3 x z\right)\right)} = {\color{red}\left(3 x \frac{d}{dz} \left(z\right)\right)}$$套用冪次法則 $$$\frac{d}{dz} \left(z^{n}\right) = n z^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{dz} \left(z\right) = 1$$$：
$$3 x {\color{red}\left(\frac{d}{dz} \left(z\right)\right)} = 3 x {\color{red}\left(1\right)}$$因此，$$$\frac{d}{dz} \left(3 x z\right) = 3 x$$$。
答案
$$$\frac{d}{dz} \left(3 x z\right) = 3 x$$$A
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