function yp = humps_ode ( x, y )

%*****************************************************************************80
%
%% humps_ode() evaluates the derivative of the humps function for an ODE solver.
%
%  Discussion:
%
%    This verion of "humps_deriv" appends the input argument "y", as expected 
%    by most ODE solving software.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    30 July 2019
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real x(): the arguments.
%
%    real y(): the value of the humps function.
%
%  Output:
%
%    real yp(): the value of the derivative of the humps function.
%
  yp = - 1.0 ./ ( ( x - 0.3 ).^2 + 0.01 ).^2 ...
      .* 2.0 .* ( x - 0.3 ) ...
      - 1.0 ./ ( ( x - 0.9 ).^2 + 0.04 ).^2 ...
      .* 2.0 .* ( x - 0.9 );

  return
end
