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An important problem of optimization analysis surges when parameters such as$ \{\theta_j\}_{j=1,\, \dots \,,k }$, determining a function $y=f(x\given\{\theta_j\}) $, must be estimated from a set of observables $ \{x_i,y_i\}_{i=1,\, \dots \,,m} $. Where $ \{x_i\} $ are independent variablesassumed to be uncertainty-free. It is known that analytical solutions arepossible if $ y=f(x\given\theta_j) $ is a linear combination of $\{\theta_{j=1,\, \dots \,,k} \}.$ Here it is proposed that determining theuncertainty of parameters that are not \textit{linearly independent} may beachieved from derivatives $ \tfrac{\partial f(x \given \{\theta_j\})}{\partial\theta_j} $ at an optimum, if the parameters are \textit{stochasticallyindependent}.

First derivatives at the optimum analysis (\textit{fdao}): An approach  to estimate the uncertainty in nonlinear regression involving stochastically  independent variables