Although the derivation above is elementary, the approach can also be viewed from a more conceptual perspective so that the result becomes more apparent. Indeed the difference operators Δ Δ x t , Δ Δ y t commute and Δ Δ x t f , Δ Δ y t f tend to ∂ ∂ x f , ∂ ∂ y f as t tends to 0, with a similar statement for second order operators. Here, for z a vector in the plane and u a directional vector ( 1 0 ) or ( 0 1 ) , the difference operator is defined by