code: def derivatives(self, x, y, coeffs, beta, center_x=0, center_y=0):
          
          shapelets = self._createShapelet(coeffs)
          r, phi = param_util.cart2polar(x, y, center=np.array([center_x, center_y]))
          alpha1_shapelets, alpha2_shapelets = self._alphaShapelets(shapelets, beta)
          f_x = self._shapeletOutput(r, phi, beta, alpha1_shapelets)
          f_y = self._shapeletOutput(r, phi, beta, alpha2_shapelets)
          return f_x, f_y
docs: returns df/dx and df/dy of the function