Solution 1.2:1e

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The quotient rule gives

\displaystyle \begin{align}

\Bigl(\frac{x}{\ln x}\Bigr)' &= \frac{(x)'\cdot \ln x - x\cdot (\ln x)'}{(\ln x)^2}\\[5pt] &= \frac{1\cdot\ln x - x\cdot\dfrac{1}{x}}{(\ln x)^2}\\[5pt] &= \frac{\ln x-1}{(\ln x)^2}\\[5pt] &= \frac{1}{\ln x} - \frac{1}{(\ln x)^2}\,\textrm{.} \end{align}