Q85 / 180 · KCET 2007 · Mathematics

If $y=2^{\log x}$, then $\frac{d y}{d x}$ is

  • A
    $\frac{2^{\log x}}{\log 2}$
  • B
    $2^{\log x} \cdot \log 2$
  • C
    $\frac{2^{\log x}}{x}$
  • Correct answer
    D
    $\frac{2^{\log x} \cdot \log 2}{x}$

Solution

Given, $y=2^{\log x}$ $$ \begin{aligned} &\Rightarrow \quad \frac{d y}{d x}=2^{\log x} \cdot \log _{e} 2 \cdot \frac{1}{x} \quad\left[\because \frac{d}{d x}\left(a^{x}\right)=a^{x} \log _{e} a\right] \\ &\Rightarrow \quad \frac{d y}{d x}=\frac{2^{\log x} \cdot \log _{e} 2}{x} \end{aligned} $$

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

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