code: def derivatives(self, x, y, theta_E, r_trunc, center_x=0, center_y=0):
          
          x_shift = x - center_x
          y_shift = y - center_y
  
          dphi_dr = self._dphi_dr(x_shift, y_shift, theta_E, r_trunc)
          dr_dx, dr_dy = self._dr_dx(x_shift, y_shift)
          f_x = dphi_dr * dr_dx
          f_y = dphi_dr * dr_dy
          return f_x, f_y
docs: returns df/dx and df/dy of the function