  We present a simple and general formalism to compute efficiently the
derivatives of a multi-determinant Jastrow-Slater wave function, the local
energy, the interatomic forces, and similar quantities needed in quantum Monte
Carlo. Through a straightforward manipulation of matrices evaluated on the
occupied and virtual orbitals, we obtain an efficiency equivalent to
algorithmic differentiation in the computation of the interatomic forces and
the optimization of the orbital paramaters. Furthermore, for a large
multi-determinant expansion, the significant computational gain recently
reported for the calculation of the wave function is here improved and extended
to all local properties in both all-electron and pseudopotential calculations.
