Question

If $y=2^{Log\,x}$, then $\frac {dy}{dx}$ is

• A. $2^{Log\,x}.Log\,2$
• B. $\frac {2^{Log\,x}}{Log\,2} $
• C. $\frac {2^{Log\,x}Log\,2}{x} $
• D. $\frac {2^{Log\,x}}{x} $

Answer 1

Answer: (C)

Given, $y = 2^{\log x} $
$ \Rightarrow \frac{dy}{dx} = 2^{\log x} . \log_{e} 2. \frac{1}{x} $
$ \left[\because \frac{d}{dx} \left(a^{x} \right) = a^{x} \log_{e} a\right] $
$ \Rightarrow \frac{dy}{dx} = \frac{2^{\log x} . \log_{e}2}{x} $