$$$\frac{\ln\left(a\right)}{\ln\left(b\right)}$$$ 关于 $$$a$$$ 的导数
相关计算器: 对数求导法计算器, 带步骤的隐函数求导计算器
您的输入
求$$$\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right)$$$。
解答
对 $$$c = \frac{1}{\ln\left(b\right)}$$$ 和 $$$f{\left(a \right)} = \ln\left(a\right)$$$ 应用常数倍法则 $$$\frac{d}{da} \left(c f{\left(a \right)}\right) = c \frac{d}{da} \left(f{\left(a \right)}\right)$$$：
$${\color{red}\left(\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right)\right)} = {\color{red}\left(\frac{\frac{d}{da} \left(\ln\left(a\right)\right)}{\ln\left(b\right)}\right)}$$自然对数的导数为 $$$\frac{d}{da} \left(\ln\left(a\right)\right) = \frac{1}{a}$$$：
$$\frac{{\color{red}\left(\frac{d}{da} \left(\ln\left(a\right)\right)\right)}}{\ln\left(b\right)} = \frac{{\color{red}\left(\frac{1}{a}\right)}}{\ln\left(b\right)}$$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