code: def derivatives(self, x, y, center_x = 0, center_y = 0, **kwargs):
  
          
  
          assert 'norm' in kwargs.keys(), "key word arguments must contain 'norm', " \
                                          "the normalization of deflection angle in units of arcsec."
  
          x_ = x - center_x
          y_ = y - center_y
          R = np.sqrt(x_**2 + y_**2)
  
          alpha = self._interp(x_, y_, **kwargs)
  
          cos_theta = x_ * R ** -1
          sin_theta = y_ * R ** -1
  
          f_x, f_y = alpha * cos_theta, alpha * sin_theta
  
          return f_x, f_y
docs: returns df/dx and df/dy (un-normalized!!!) interpolated from the numerical deflection table