+ ##
+ ## INPUTS:
+ ##
+ ## * ``integer_order`` - The order of the derivative which we're
+ ## approximating.
+ ##
+ ## * ``xs`` - The vector of x-coordinates.
+ ##
+ ## * ``x`` - The point `x` at which you'd like to evaluate the
+ ## derivative of the specified `integer_order`. This should be an
+ ## element of `xs`.
+ ##
+ ##
+ ## OUTPUTS:
+ ##
+ ## * ``coefficients`` - The vector of coefficients, in order, of
+ ## f(x0), f(x1), ..., f(xn).
+ ##
+
+ if (integer_order < 0)
+ ## You have made a grave mistake.
+ df = NA;
+ return;
+ end
+