Solution 1.2:1e
From Förberedande kurs i matematik 2
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| - | {{ | + | The quotient rule gives |
| - | + | ||
| - | {{ | + | {{Displayed math||<math>\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}</math>}} | ||
Current revision
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} |
