f'(x) = [-1/(x*lnx)^2] * (x * lnx)'= [-1/(x*lnx)^2] * [x * (lnx)' + x' * lnx]= [-1/(x*lnx)^2] * [x * (1/x) + lnx]= [-1/(x*lnx)^2] * (1 + lnx)= -(1 + lnx)/(x lnx)^2