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$$$6 x e^{3}$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(6 x e^{3}\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$，使用 $$$c = 6 e^{3}$$$ 與 $$$f{\left(x \right)} = x$$$：
$${\color{red}\left(\frac{d}{dx} \left(6 x e^{3}\right)\right)} = {\color{red}\left(6 e^{3} \frac{d}{dx} \left(x\right)\right)}$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{dx} \left(x\right) = 1$$$：
$$6 e^{3} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = 6 e^{3} {\color{red}\left(1\right)}$$因此，$$$\frac{d}{dx} \left(6 x e^{3}\right) = 6 e^{3}$$$。
答案
$$$\frac{d}{dx} \left(6 x e^{3}\right) = 6 e^{3}$$$A
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