function J = p24_j ( m, n, x )

%*****************************************************************************80
%
%% p24_j() evaluates the jacobian for problem 24.
%
%  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 : m

    ti = ( i - 1 ) / 10.0;

    J(i,1) = x(2)^ti * sin ( x(3) * ti + x(4) );
    J(i,2) = x(1) * ti * x(2)^( ti - 1.0 ) * sin ( x(3) * ti + x(4) );
    J(i,3) = x(1) * x(2)^ti * ti * cos ( x(3) * ti + x(4) );
    J(i,4) = x(1) * x(2)^ti * cos ( x(3) * ti + x(4) );

  end

  return
end
