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$$$\frac{\ln\left(x\right)}{\ln\left(2\right)}$$$的导数
您的输入
求$$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right)$$$。
解答
对 $$$c = \frac{1}{\ln\left(2\right)}$$$ 和 $$$f{\left(x \right)} = \ln\left(x\right)$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dx} \left(\ln\left(x\right)\right)}{\ln\left(2\right)}\right)}$$自然对数的导数为 $$$\frac{d}{dx} \left(\ln\left(x\right)\right) = \frac{1}{x}$$$：
$$\frac{{\color{red}\left(\frac{d}{dx} \left(\ln\left(x\right)\right)\right)}}{\ln\left(2\right)} = \frac{{\color{red}\left(\frac{1}{x}\right)}}{\ln\left(2\right)}$$因此，$$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right) = \frac{1}{x \ln\left(2\right)}$$$。
答案
$$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right) = \frac{1}{x \ln\left(2\right)}$$$A
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