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If $y=2^{x / \ln x}$ then $\frac{d y}{d x}$ at $x=e$ is
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$\log y=\frac{x}{\log x} \log 2$
$\left.\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}\right]_{\mathrm{x}=\mathrm{e}}=0$
$\left.\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}\right]_{\mathrm{x}=\mathrm{e}}=0$
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