The derivatives should be:
d f d t ( t ) = − 2 t ( 1 + t 2 ) 2 {\displaystyle {\frac {df}{dt}}(t)=-{\frac {2t}{(1+t^{2})^{2}}}}
d 2 f d t 2 ( t ) = 6 t 2 ( 1 + t 2 ) 3 − 2 ( 1 + t 2 ) 3 {\displaystyle {\frac {d^{2}f}{dt^{2}}}(t)={\frac {6t^{2}}{(1+t^{2})^{3}}}-{\frac {2}{(1+t^{2})^{3}}}}
d 3 f d t 3 ( t ) = − 24 t 3 ( 1 + t 2 ) 4 + 24 t ( 1 + t 2 ) 4 {\displaystyle {\frac {d^{3}f}{dt^{3}}}(t)=-{\frac {24t^{3}}{(1+t^{2})^{4}}}+{\frac {24t}{(1+t^{2})^{4}}}}
Return to errata.
