ln(x)/ln(2) 的導數

此計算器將求出 $$$\frac{\ln\left(x\right)}{\ln\left(2\right)}$$$ 的導數，並顯示步驟。

您的輸入

求$$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right)$$$。

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 $$$c = \frac{1}{\ln\left(2\right)}$$$ 與 $$$f{\left(x \right)} = \ln\left(x\right)$$$：

$${\color{red}\left(\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dx} \left(\ln\left(x\right)\right)}{\ln\left(2\right)}\right)}$$

自然對數的導數為 $$$\frac{d}{dx} \left(\ln\left(x\right)\right) = \frac{1}{x}$$$：

$$\frac{{\color{red}\left(\frac{d}{dx} \left(\ln\left(x\right)\right)\right)}}{\ln\left(2\right)} = \frac{{\color{red}\left(\frac{1}{x}\right)}}{\ln\left(2\right)}$$

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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