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I esuselwe sine ye-engeli ilingana cosine ye-engeli efanayo
Dana elula trigonometry umsebenzi y = Sin (x), kuyinto differentiable iphoyinti yonke domain ngamunye. Kufanele zifakazela ukuthi le esuselwe sine yanoma iyiphi i-agumenti ithi ilingane cosine engela efanayo, okungukuthi, '= Cos (x).
Ubufakazi kusekelwe kwencazelo umsebenzi esuselwe
Sichaza x (ngokungenasizathu) kwezinye endaweni encane iphuzu elithile x Δh 0. Siyobonisa ukubaluleka umsebenzi kuwo, futhi ngesikhathi x iphuzu ukuthola anyuswe yomsebenzi inikezwe. Uma Δh - agumenti bakhuphula, i-agumenti okusha - x 0 + Δx = x, ukubaluleka lo msebenzi wenani kunikezwa agumenti (x) ilingana Sin (x 0 + Δx), inani umsebenzi weyesi ethize (x 0) kubuye ezaziwayo .
Manje sinesizathu Δu = Sin (x 0 + Δh) -Sin (x 0) - etholwe anyuswe umsebenzi.
Ngokusho formula isamba sine ye-engeli amabili ukungalingani sizobe ukuguqula umehluko Δu.
Δu = Sin (x 0) · Cos (Δh) + Cos (x 0) · Sin (Δx) lokususa Sin (x 0) = (Cos (Δx) -1 ) · Sin ( x 0) + Cos (x 0) · Sin (Δh).
Okwenziwe permutation imigomo babeqoqana ngowokuqala Sin wesithathu (x 0), ithathwa isici esivamile - sine - kubakaki. Sithole ethi Cos umehluko (Δh) -1. It kwesokunxele ukushintsha uphawu phambi abakaki kanye kubakaki. Ngokwazi lokho okuthenjiswa 1-Cos (Δh), senza ushintsho futhi ukuthola Δu Inkulumo lula, okuyinto ke ehlukaniswa Δh.
Δu / Δh kuyodingeka ifomu: Cos (x 0) · Sin (Δh) / Δh 2 · Sin 2 (0.5 x Δh) · Sin (x 0) / Δh. Lona isilinganiso anyuswe umsebenzi kuya yokwemukela anyuswe lwempikiswano.
It uhlala ukuthola umkhawulo we okungu etholwe nathi ngesikhathi Δh lim, elusa zero.
Kuyaziwa ukuthi umkhawulo Sin (Δh) / Δx ilingana 1, ngaphansi kombandela. Namazwi 2 · Sin 2 (0.5 x Δh) / Δh ku okuholela isamba kugucuka ethile umkhiqizo aqukethe njengoba Okuphindaphinda kuqala umkhawulo esimangalisayo: the numerator we ingxenyenamba futhi znemenatel hlukanisa imali yazo ngo 2, esigcawini sine esikhundleni umkhiqizo. Nansi indlela:
(Sin (0,5 · Δx) / (0,5 · Δx)) · Sin (Δx / 2).
Umkhawulo le nkulumo lapho Δh ivame kuqanda, kuyoba ilingana nenani oholayo (0 iphindwe 1). It kuvela ukuthi umkhawulo we isilinganiso Δy / Δh kuyinto Cos (x 0) · 1-0, lokhu Cos (x 0), inkulumo ethi okuyinto ozimele Δh elusa 0. Isiphetho: i-esuselwe sine yanoma iyiphi i-engeli ilingana x cosine x, singatlolwa bunjesi: y '= Cos (x).
Ifomula okuholela is ezisohlwini ithebula lama-derivatives eyaziwa, lapho yonke imisebenzi aphansi
Ekuxazululeni izinkinga, lapho uhlangana esuselwe sine, ungasebenzisa imithetho yokuzihlukanisa kwamangqamuzana ngokwemisebenzi yawo kanye namafomula ngomumo-ezenziwe etafuleni. Ngokwesibonelo: ukuthola esuselwe elula umsebenzi y = 3 · Sin (x) -15. Sisebenzisa aphansi imithetho bheke ukususwa isici kwamanani for isibonakaliso esuselwe futhi abale isibalo esuselwe njalo (okuyinto oyigungqu). Sebenzisa sine itafula inani le esuselwe engela x Cos alinganayo (x). Thola impendulo: y '= 3 · Cos (x) -O. Lokhu esuselwe, esikhundleni salokho, nalo liyisifo esithathelana aphansi umsebenzi y = H · Cos (x).
I esuselwe sine yisikwele kwanoma iyiphi ingxabano
Ngo ukubala okuvela kuyo le nkulumo (Sin 2 (x)) 'Kumelwe ukhumbule ukuthi umahluko umsebenzi eziyinkimbinkimbi. Ngakho, 2 = Sin (x) - umsebenzi amandla njengoba sine yisikwele. agumenti yayo futhi umsebenzi Trigonometric, i-agumenti eziyinkimbinkimbi. Umphumela kulokhu elilingana umkhiqizo multiplier sokuqala isikwele we esuselwe eyinkimbinkimbi agumenti, kanti owesibili - the esuselwe sine. Nakhu isimiso umehluko umsebenzi umsebenzi: (u (v (x))) 'is (u (v (x)))' · (v (x)). Ukubonakaliswa Komusa v (x) - i-agumenti eziyinkimbinkimbi (umsebenzi yangaphakathi). Uma umsebenzi anikezwe "y lilingana sine yisikwele x", ke esuselwe kule umsebenzi esiyinhlanganisela kuyinto y '= 2 · Sin (x) · Cos (x). Umkhiqizo we Okuphindaphinda wokuqala kabili - esuselwe eyaziwa umsebenzi lomchazi, futhi Cos (x) - itheku esuselwe agumenti eziyinkimbinkimbi we umsebenzi quadratic. Umphumela wokugcina kungenziwa siguqulwe ngokusebenzisa formula sine Trigonometric ye-engeli double. A: I-esuselwe kuyinto Sin (2 · x). Lokhu ifomula okulula ukuyikhumbula, ke livame ukusetshenziswa njengoba itafula.
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