Test

\begin{aligned} \frac{d^{2}}{d x^{2}} \ln f (x) & = \frac{f^{″} (x)}{f (x)} - {(\frac{f^{'} (x)}{f (x)})}^{2} \\ \frac{d^{3}}{d x^{3}} \ln f (x) & = \frac{f^{(3)} (x)}{f (x)} - 3 \frac{f^{'} (x) f^{″} (x)}{f {(x)}^{2}} + 2 {(\frac{f^{'} (x)}{f (x)})}^{3} \\ \frac{d^{4}}{d x^{4}} \ln f (x) & = \frac{f^{(4)} (x)}{f (x)} - 4 \frac{f^{'} (x) f^{(3)} (x)}{f {(x)}^{2}} - 3 {(\frac{f^{″} (x)}{f (x)})}^{2} + 12 \frac{f^{'} {(x)}^{2} f^{″} (x)}{f {(x)}^{3}} - 6 ( \end{aligned}

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