y=xlnx/(x+1)-ln(x+1)y'=[(xlnx)'(x+1)-xlnx(x+1)']/(x+1)^2-1/(x+1)=[(lnx+1)(x+1)-xlnx]/(x+1)^2-1/(x+1)=(xlnx+lnx+x+1-xlnx)/(x+1)^2-1/(x+1)=[(1+x+lnx)-(x+1)]/(x+1)^2=lnx/(x+1)^2.