Źródło TeX:

f^{\prime }(x)=(\frac{1}{x}+2\operatorname{arctg}x)^{\prime }=-\frac{1}{x^{2}}+ \frac{2}{x^{2}+1}=\frac{x^{2}-1}{x^{2}\left( x^{2}+1\right) }=\frac{ \left( x-1\right) \left( x+1\right) }{x^{2}\left( x^{2}+1\right) }