Q74 / 120 · VITEEE 2016 · Mathematics

If $y=2^{x / \ln x}$ then $\frac{d y}{d x}$ at $x=e$ is

  • A
    $\mathrm{e}$
  • B
    $2^{\mathrm{e}} \log 2$
  • C
    $\log 2$
  • Correct answer
    D
    0

Solution

$\log y=\frac{x}{\log x} \log 2$ $\left.\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}\right]_{\mathrm{x}=\mathrm{e}}=0$

Hence, the correct answer is option: 'D'.

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