y=xtanxlnx
y'=(xtanx)'lnx+xtanx(lnx)'
=x'tanxlnx+x(tanx)'lnx+xtanx*1/x
=tanxlnx+x*sec^2x lnx+tanx
=tanx(lnx+1)+xsec^2x*lnx