function value = runge_deriv ( x )

%*****************************************************************************80
%
%% runge_deriv() evaluates the derivative of the Runge function.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    23 March 2025
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real x: the argument of the function.
%
%  Output:
%
%    real value: the value of the derivative.
%
  value = - 50.0 * x ./ ( 1.0 + 25.0 * x .* x ).^2;

  return
end
