Question

If $y=\log (\log x)$ then the value of $e^y\frac{dy}{dx}$ is

• A. $e^y$
• B. $\frac{1}{x}$
• C. $\frac{1}{(\log x)}$
• D. $\frac{1}{(x\log x)}$

Answer 1

Answer: (B)

Let $y=\log (\log x)$
Diff both side w.r.t ${}^{\prime }{x}^{\prime }$, we get
$\frac{dy}{dx}=\frac{1}{logx}\frac{d}{dx}(\log x)$
$\Rightarrow \frac{dy}{dx}=\frac{1}{\log x}\times \frac{1}{x}$
$\Rightarrow \log x.\frac{dy}{dx}=\frac{1}{x}$
$\Rightarrow e^y\frac{dy}{dx}=\frac{1}{x}$
$(\because e^y=e^{\log (\log x)}=\log x)$