Question

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

• A. $2^{Logx}.Log2$
• B. $\frac{2^{Logx}}{Log2}$
• C. $\frac{2^{Logx}Log2}{x}$
• D. $\frac{2^{Logx}}{x}$

Answer 1

Answer: (C)

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