d1 <- function (x , y)
{
  ## Purpose: primitive 1. Ableitung
  ## ----------------------------------
  ## Author: Martin Maechler, Jun 96
  n <- length(y)
  if(n != length(x)) stop("lengths of 'x' & 'y' must equal")
  
   c(y[2] - y[1], 0.5 * (y[ -(1:2)] - y[ -((n-1):n)]), y[n] - y[n-1]) /
   c(x[2] - x[1], 0.5 * (x[ -(1:2)] - x[ -((n-1):n)]), x[n] - x[n-1])
}