Źródło TeX:

f^\prime(x)=\frac{\frac1x\left(1+\ln^2x\right)-\ln x\cdot 2\ln x\cdot\frac1x}{\left(1+\ln^2 x\right)^2}= \frac{1-\ln^2 x}{x\left(1+\ln^2 x\right)^2}, \; x\in (0, +\infty)