code: def derivatives(self, x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0):
          
          phi_G, q = param_util.ellipticity2phi_q(e1, e2)
          e = abs(1. - q)
          cos_phi = np.cos(phi_G)
          sin_phi = np.sin(phi_G)
          x_, y_ = self._coord_transf(x, y, q, phi_G, center_x, center_y)
          f_x_prim, f_y_prim = self.sersic.derivatives(x_, y_, n_sersic, R_sersic, k_eff)
          f_x_prim *= np.sqrt(1 - e)
          f_y_prim *= np.sqrt(1 + e)
          f_x = cos_phi*f_x_prim-sin_phi*f_y_prim
          f_y = sin_phi*f_x_prim+cos_phi*f_y_prim
          return f_x, f_y
docs: returns df/dx and df/dy of the function