code: def derivatives(self, x, y, amp, sigma, center_x=0, center_y=0):
          
          x_ = x - center_x
          y_ = y - center_y
          R = np.sqrt(x_**2 + y_**2)
          sigma_x, sigma_y = sigma, sigma
          if isinstance(R, int) or isinstance(R, float):
              R = max(R, self.ds)
          else:
              R[R <= self.ds] = self.ds
          alpha = self.alpha_abs(R, amp, sigma)
          return alpha / R * x_, alpha / R * y_
docs: returns df/dx and df/dy of the function