code: def derivatives(self, x, y, n_sersic, R_sersic, k_eff, center_x=0, center_y=0):
          
          x_ = x - center_x
          y_ = y - center_y
          r = np.sqrt(x_**2 + y_**2)
          if isinstance(r, int) or isinstance(r, float):
              r = max(self._s, r)
          else:
              r[r < self._s] = self._s
          alpha = -self.alpha_abs(x, y, n_sersic, R_sersic, k_eff, center_x, center_y)
          f_x = alpha * x_ / r
          f_y = alpha * y_ / r
          return f_x, f_y
docs: returns df/dx and df/dy of the function