code: def derivatives(self, x, y, Rs, theta_Rs, r_core, center_x=0, center_y=0):
          
  
          rho0 = self._alpha2rho0(theta_Rs=theta_Rs, Rs=Rs, r_core=r_core)
  
          if Rs < 0.0000001:
              Rs = 0.0000001
          x_ = x - center_x
          y_ = y - center_y
          R = np.sqrt(x_ ** 2 + y_ ** 2)
  
          dx, dy = self.coreBurkAlpha(R, Rs, rho0, r_core, x_, y_)
  
          return dx, dy
docs: deflection angles
          :param x: x coordinate
          :param y: y coordinate
          :param Rs: scale radius
          :param rho0: central core density
          :param r_core: core radius
          :param center_x:
          :param center_y:
          :return: