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$$$3 \ln\left(x\right)$$$的导数
您的输入
求$$$\frac{d}{dx} \left(3 \ln\left(x\right)\right)$$$。
解答
对 $$$c = 3$$$ 和 $$$f{\left(x \right)} = \ln\left(x\right)$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(3 \ln\left(x\right)\right)\right)} = {\color{red}\left(3 \frac{d}{dx} \left(\ln\left(x\right)\right)\right)}$$自然对数的导数为 $$$\frac{d}{dx} \left(\ln\left(x\right)\right) = \frac{1}{x}$$$：
$$3 {\color{red}\left(\frac{d}{dx} \left(\ln\left(x\right)\right)\right)} = 3 {\color{red}\left(\frac{1}{x}\right)}$$因此，$$$\frac{d}{dx} \left(3 \ln\left(x\right)\right) = \frac{3}{x}$$$。
答案
$$$\frac{d}{dx} \left(3 \ln\left(x\right)\right) = \frac{3}{x}$$$A
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