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$$$2 \ln\left(x\right)$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(2 \ln\left(x\right)\right)$$$。
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 $$$c = 2$$$ 與 $$$f{\left(x \right)} = \ln\left(x\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(2 \ln\left(x\right)\right)\right)} = {\color{red}\left(2 \frac{d}{dx} \left(\ln\left(x\right)\right)\right)}$$自然對數的導數為 $$$\frac{d}{dx} \left(\ln\left(x\right)\right) = \frac{1}{x}$$$：
$$2 {\color{red}\left(\frac{d}{dx} \left(\ln\left(x\right)\right)\right)} = 2 {\color{red}\left(\frac{1}{x}\right)}$$因此，$$$\frac{d}{dx} \left(2 \ln\left(x\right)\right) = \frac{2}{x}$$$。
答案
$$$\frac{d}{dx} \left(2 \ln\left(x\right)\right) = \frac{2}{x}$$$A
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