Sensitivity analysis for feedforward artificial neural networks with differentiable activation functions

A method for computing the network output sensitivities with respect to variations in the inputs for multilayer feedforward artificial neural networks with differentiable activation functions is presented. It is applied to obtain expressions for the first- and second-order sensitivities. An example is introduced along with a discussion to illustrate how the sensitivities are calculated and to show how they compare to the actual derivatives of the function being modeled by the neural network