function J = p08_j ( m, n, x )

%*****************************************************************************80
%
%% p08_j() evaluates the jacobian for problem 8.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%  Modified:
%
%    03 March 2026
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, the number of equations.
%
%    integer N, the number of variables.
%
%    real X(N), the evaluation point.
%
%  Output:
%
%    real J(M,N), the jacobian matrix.
%
  J = zeros ( m, n );

  for i = 1 : 15

    tmp1 = i;
    tmp2 = 16 - i;
    if ( i <= 8 )
      tmp3 = tmp1;
    else
      tmp3 = tmp2;
    end

    J(i,1) = - 1.0;
    J(i,2) = tmp1 * tmp2 / ( x(2) * tmp2 + x(3) * tmp3 )^2;
    J(i,3) = tmp1 * tmp3 / ( x(2) * tmp2 + x(3) * tmp3 )^2;

  end

  return
end
