$\log_{a} x$ の微分
\begin{eqnarray*} y&=&\log_{a} x\\ &=& \frac{\log x}{\log a}\\ &=& \frac{\log 'x \log a - \log x \log 'a}{\log^{2}a}\\ &=& \frac{\frac{1}{x}\log a}{\log^{2}a}\\ &=& \frac{1}{x\log a} \end{eqnarray*}
\begin{eqnarray*} y&=&\log_{a} x\\ &=& \frac{\log x}{\log a}\\ &=& \frac{\log 'x \log a - \log x \log 'a}{\log^{2}a}\\ &=& \frac{\frac{1}{x}\log a}{\log^{2}a}\\ &=& \frac{1}{x\log a} \end{eqnarray*}