{1/2・log(1+x^2)}'=log{1/(1+x^2)^1/2}={1/(1+x^2)^1/2}{(1+x^2)^1/2}'
={1/(1+x^2)^1/2}(2x)/{2√(1+x^2)}
=x/(1+x^2)

{1/2・log(1+x^2)}'=1/2・1/(1+x^2)・(1+x^2)'=(1/2)(2x)/(1+x^2)=x/(1+x^2)