If $y =log_2(log_2x),$ then $\frac{dy}{dx}$ is equal to :

$\frac{log_2e}{xlog_ex}$

$y=\log_2(\log_2 x)$

$y=\frac{\ln(\log_2 x)}{\ln 2}$

$\frac{dy}{dx}=\frac{1}{\ln 2}\cdot \frac{1}{\log_2 x}\cdot \frac{d}{dx}(\log_2 x)$

$\frac{d}{dx}(\log_2 x)=\frac{1}{x\ln 2}$

$\frac{dy}{dx}=\frac{1}{\ln 2}\cdot \frac{1}{\log_2 x}\cdot \frac{1}{x\ln 2}$

$=\frac{1}{x(\ln 2)^2 \log_2 x}$

$\log_2 x=\frac{\ln x}{\ln 2}$

$\frac{dy}{dx}=\frac{1}{x\ln 2 \cdot \ln x}$

$\frac{dy}{dx}=\frac{1}{x\ln 2 \cdot \ln x}$