Mathematical　derivatives　can　be　approximated　or　calculated　by　the　techniques　including　symbolic　differentiation,　divided　difference,　and　automatic　differentiation　etc.　Automatic　differentiation　(AD)　can　compute　fast　and　accurate　derivatives　such　as　the　Jacobian,　Hessian　matrix　and　the　tensor　of　the　function.　One　of　the　most　important　applications　is　to　improve　the　optimization　algorithms　by　computing　the　relevant　derivative　information　efficiently.　In　this　paper,　AD　algorithms　computing　the　Hessian　and　tensor　terms　are　given,　and　their　computational　complexity　is　investigated　Furthermore,　they　are　applied　to　Chebyshev＇s　method,　which　includes　the　evaluation　of　the　tensor　terms.　The　experiment　results　show　that　AD　can　be　used　efficiently　in　the　optimization　methods.