looote, see below: d/dx[(e^x-1).(x^{-1})] = [(e^x-1).(-1).(x^{-2})] + [(e^x).(x^{-1})] = [e^x(x-1) + 1]/x^2 x --> 0 ==> [e^x(x-1) + 1]/x^2 --> 0/0 if you think just taking derivative and then replacing x by 0 works, point out the step where i am wrong.