The well-documented inaccuracies that arise when numerical differentiation is used in scientific and engineering computations of even moderate size suggest that actual derivatives should be used instead. Human error frequently rears its head in the computation of partial derivatives of complicated vector functions. This paper presents PASCAL-SC progams needed to let a computer automatically compute derivatives (not numerical approximations thereof) or gradient vectors. The suggested PASCAL-SC subroutines were implemented and tested using a Z-80 processor (Zilog MCZ1/05 computer) with ample storage under the University of Karlsruhe (West Germany) PASCAL-SC compiler, which ran under the Zilog RI0 2.06 operating system. The well-tested system::9I was run, as an example using the gradient Newton method, with outstanding results. If your computations involve equations of this type or others that require derivative as well as function values, and for which the simpler &mgr;-math programs are inadequate, then by all means examine this paper. You will thank Rall for his Herculean effort and care.