$$$\frac{\ln\left(a\right)}{\ln\left(b\right)}$$$ 對 $$$a$$$ 的導數
相關計算器: 對數微分計算器, 隱式微分計算器（附步驟）
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求$$$\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{da} \left(c f{\left(a \right)}\right) = c \frac{d}{da} \left(f{\left(a \right)}\right)$$$，使用 $$$c = \frac{1}{\ln\left(b\right)}$$$ 與 $$$f{\left(a \right)} = \ln\left(a\right)$$$：
$${\color{red}\left(\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right)\right)} = {\color{red}\left(\frac{\frac{d}{da} \left(\ln\left(a\right)\right)}{\ln\left(b\right)}\right)}$$自然對數的導數為 $$$\frac{d}{da} \left(\ln\left(a\right)\right) = \frac{1}{a}$$$：
$$\frac{{\color{red}\left(\frac{d}{da} \left(\ln\left(a\right)\right)\right)}}{\ln\left(b\right)} = \frac{{\color{red}\left(\frac{1}{a}\right)}}{\ln\left(b\right)}$$因此，$$$\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right) = \frac{1}{a \ln\left(b\right)}$$$。
答案
$$$\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right) = \frac{1}{a \ln\left(b\right)}$$$A