Find second order derivative of `log(logx)`

Explanation

Let `y=\log (\log x)`



`\Rightarrow \frac{d y}{d x}=\frac{d}{d x}[\log (\log x)]=\frac{1}{\log x} \cdot \frac{d}{d x}(\log x)=\frac{1}{x \log x}=(x \log x)^{-1} `



`\therefore \frac{d^{2} y}{d x^{2}}=\frac{d}{d x}[(x \log x)^{-1}]=(-1) \cdot(x \log x)^{-2} \cdot \frac{d}{d x}(x \log x) `


...