  We propose a simple recursive algorithm that allows the computation of the
first- and second-order derivatives with respect to the inputs of an arbitrary
deep feed forward neural network (DFNN). The algorithm naturally incorporates
the derivatives with respect to the network parameters. To test the algorithm,
we apply it to the study of the quantum mechanical variational problem for few
cases of simple potentials, modeling the ground-state wave function in terms of
a DFNN.
