A Simple Automatic Derivative Evaluation Program
A procedure for automatic evaluation of total/partial
derivatives of arbitrary algebraic functions 
is presented.  The technique permits computation of
numerical values of derivatives without developing 
analytical expressions for the derivatives.  The key
to the method is the decomposition of the given 
function, by introduction of intermediate variables,
into a series of elementary functional steps.  A 
library of elementary function subroutines is provided
for the automatic evaluation and differentiation 
of these new variables.  The final step in this process
produces the desired function's derivative.  
The main feature of this approach is its simplicity.
 It can be used as a quick-reaction tool where the 
derivation of analytical derivatives is laborious and
also as a debugging tool for programs which contain 
derivatives.
CACM August, 1964
Wengert, R. E.
