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If $y=2^{\log x}$, then $\frac{d y}{d x}$ is
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Verified Answer
The correct answer is:
$\frac{2^{\log x} \cdot \log 2}{x}$
Given, $y=2^{\log x}$
$$
\begin{aligned}
&\Rightarrow \quad \frac{d y}{d x}=2^{\log x} \cdot \log _{e} 2 \cdot \frac{1}{x} \quad\left[\because \frac{d}{d x}\left(a^{x}\right)=a^{x} \log _{e} a\right] \\
&\Rightarrow \quad \frac{d y}{d x}=\frac{2^{\log x} \cdot \log _{e} 2}{x}
\end{aligned}
$$
$$
\begin{aligned}
&\Rightarrow \quad \frac{d y}{d x}=2^{\log x} \cdot \log _{e} 2 \cdot \frac{1}{x} \quad\left[\because \frac{d}{d x}\left(a^{x}\right)=a^{x} \log _{e} a\right] \\
&\Rightarrow \quad \frac{d y}{d x}=\frac{2^{\log x} \cdot \log _{e} 2}{x}
\end{aligned}
$$
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