% Compute the derivative of shape functions respect NATURAL COORDINATES...
% ... [ji nu]
% INPUT: chi=[chi(1) chi(2)]=[ji nu] ...
% ... where the natural derivatives will be evaluated
% OUTPUT: is a matrix 4x2 containing the derivatives (see nd below)
function nd=natural_deriv_2D4N(chi)
  ji=chi(1);nu=chi(2);
  d1_N1=-(1/4)*(1-nu);
  d2_N1=-(1/4)*(1-ji);
  d1_N2=+(1/4)*(1-nu);
  d2_N2=-(1/4)*(1+ji);
  d1_N3=+(1/4)*(1+nu);
  d2_N3=+(1/4)*(1+ji);
  d1_N4=-(1/4)*(1+nu);
  d2_N4=+(1/4)*(1-ji);
  nd=[d1_N1 d2_N1 ; d1_N2 d2_N2; d1_N3  d2_N3; d1_N4 d2_N4];
return
end