y'=((1+x^2)arctanx-lnx/ln2)'=((1+x^2)arctanx)'-(lnx/ln2)'=(1+x^2)'arctanx+(1+x^2)(arctanx)'+(lnx/ln2)'=2xarctanx+(1+x^2)/(1+x^2)+1/(xln2)=2xarctanx+1+1/(xln2).