Answer
$$y'=\frac{1}{x\ln x\ln(\ln x)}$$
Work Step by Step
$$y=\ln\Big(\ln(\ln x)\Big)$$
Recall the following Derivative Rules: $$\frac{d}{dx}(\ln u)=\frac{1}{u}\frac{du}{dx}$$
We have $$y'=\Big[\ln\Big(\ln(\ln x)\Big)\Big]'=\frac{1}{\ln(\ln x)}\Big(\ln(\ln x)\Big)'$$
$$y'=\frac{1}{\ln(\ln x)}\times\frac{1}{\ln x}(\ln x)'$$
$$y'=\frac{1}{\ln(\ln x)}\times\frac{1}{\ln x}\times\frac{1}{x}$$
$$y'=\frac{1}{x\ln x\ln(\ln x)}$$
