Q100 / 180 · COMEDK 2020 · Mathematics
If $y=2^{\log x}$, then $\frac{d y}{d x}$ is
- A$2^{\log x} \cdot \log 2$
- B$\frac{2^{\log x}}{\log 2}$
- Correct answerC$\frac{2^{\log x} \log 2}{x}$
- D$\frac{2^{\log x}}{x}$
Solution
We have,
$$
\begin{gathered}
y=2^{\log x} \\
\therefore \quad \frac{d y}{d x}=2^{\log x} \cdot \log 2 \cdot \frac{d}{d x}(\log x)=\frac{2^{\log x} \log 2}{x}
\end{gathered}
$$
Hence, the correct answer is option: 'C'.