The object of talk is the differentiability of implicitly defined functions which we encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild (1997, 2001) and Murphy and Vaart (2000) developed methodologies that can avoid dealing with such implicitly defined functions by reparametrizing parameters in the profile likelihood and using an approximate least favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach developed in Hirose (2010) which uses the differentiability of implicitly defined functions.