B.-Y. Chen [7] derived an explicit formula for the Hessian determinants of composite functions defined by $f=F(h_1(x_1)+\cdots+h_n(x_n))$. In this paper, we introduce a new formula for the Hessian determinants of composite functions of the form \[ f=F(h_1(x_1)\times\cdots\times h_n(x_n)) \] Several applications of the new formula to the well-known Cobb-Douglas production functions in economics are also given.