Stochastic characterizations of functions subject to constraints result in treating them as functions with non-independent variables. Using the distribution function or copula of the input variables that comply with such constraints, we derive two types of partial derivatives of functions with non-independent variables (i.e., actual and dependent derivatives) and argue in favor of the latter. Dependent partial derivatives of functions with non-independent variables rely on the dependent Jacobian matrix of non-independent variables, which is also used to dene a tensor metric. The dif- ferential geometric framework allows for deriving the gradient, Hessian and Taylor-type expansion of functions with non-independent variables.