\(\displaystyle L(x,\phi)=\log{\phi}+\log{\log{\phi}}\underbrace{ - \log{(-x)}}\) \(\displaystyle \color{red}{\text{[]EDIT[] You have to incorporate the -log(-x) part since:}}\) \(\displaystyle \color{red}{\phi=e^{-\lambda x} \implies x = \frac{\log\phi}{-\lambda}}\)

\(\displaystyle \frac{d}{d\phi}L(x,\phi)=\frac{1}{\phi}+\frac{1}{\phi}\cdot\frac{1}{\log{\phi}}\color{red}{+...}\)

\(\displaystyle \frac{d^2}{d\phi^2}L(x,\phi)=-\frac{1}{\phi^2}+\left\{\frac{1}{\phi}\cdot\frac{d}{d\phi}[\frac{1}{\log{\phi}}] + \frac{1}{\log{\phi}}\cdot\frac{d}{d\phi}[\frac{1}{\phi}] \right\}\color{red}{+...}\)

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