Focusing　on　the　problem　of　architectural　design　of　extreme　learning　machine　(ELM),　we　propose　a　novel　constructive　algorithm　by　the　activation　function　and　its　derivatives.　Firstly,　taking　the　Sigmoid　function　as　an　example,　we　give　in　detail　the　derived　characteristics　for　a　class　of　base　functions:　derivative　functions　can　be　expressed　by　their　primitive　functions.　By　making　use　of　these　derived　characteristics,　we　propose　a　method　to　design　the　structure　of　ELM,　which　automatically　generate　feedforward　neural　networks　with　double　hidden　layers.　The　new　units　in　the　first　hidden　layer　are　generated　randomly　one　by　one;　then,　the　outputs　of　the　second　hidden　layer　(derivation)　are　calculated　by　the　activation　function　of　the　new　node　in　the　first　layer　and　its　derivatives.　The　weights　of　the　output　layer　are　calculated　analytically　by　the　least　squares　method.　Finally,　the　analysis　of　convergence　and　stability　are　presented.　The　effectiveness　of　the　proposed　method　is　demonstrated　by　simulation　results　on　nonlinear　system　identification　and　two-spiral　classification　problem.