Njengoba esuselwe okukhiphayo cosine

I esuselwe cosine kufana esuselwe sine ngesisekelo ubufakazi - kwencazelo umsebenzi mkhawulo. Kungenzeka ukusebenzisa enye indlela usebenzisa amafomula Trigonometric ngokushayela sine futhi cosine engeli. Veza omunye umsebenzi ngemva kwenye - ngokusebenzisa sine cosine, sine, futhi ukuhlukanisa ne-agumenti eziyinkimbinkimbi.

Cabanga ngesibonelo lokuqala ekhishwa ifomula (Cos (x)) '

Nikeza azinakwa anyuswe Δh agumenti x of y = Cos (x). Uma ukubaluleka entsha i-agumenti x + Δh ukuthola inani elisha Cos umsebenzi (x + Δh). Khona-ke ekwenyusweni Δu umsebenzi kuyoba ulingana Cos (x + Δx) -Cos (x).
Isilinganiso umsebenzi anyuswe kuyoba Δh esinjalo: (Cos (x + Δx) -Cos (x)) / Δh. Dweba ungubani kugucuka okuphumela numerator we ingxenyenamba. Khumbula ifomula umahluko cosines, umphumela uba -2Sin umsebenzi (Δh / 2) iphindwe Sin (x + Δh / 2). Sithola umkhawulo lim yangasese lo mkhiqizo nge Δh lapho Δh ivame zero. Kuyaziwa ukuthi kuqala (okuthiwa emangalisayo) umkhawulo lim (Sin (Δh / 2) / (Δh / 2)) uyalingana 1, futhi ibeke umkhawulo -Sin (x + Δh / 2) is alinganayo -Sin (x) lapho Δx, elusa zero.
Sibhala umphumela: i-esuselwe (Cos (x)) 'kuyinto - Sin (x).

Abanye bancamela indlela yesibili ka bethola indlela efanayo

Akwaziwa kusukela trigonometry: Cos (x) kuyinto Sin alinganayo (0,5 · Π-x) efanayo Sin (x) kuyinto Cos (0,5 · Π-x). Khona-ke differentiable umsebenzi eziyinkimbinkimbi - sine ye-engeli ezengeziwe (esikhundleni X cosine).
Thina ukuthola Cos umkhiqizo (0,5 · Π-x) · (0,5 · Π-x) ', ngoba esuselwe cosine sine ye x x. Ukufinyelela ifomula yesibili Sin (x) = Cos (0,5 · Π-x) esikhundleni cosine futhi sine, cabanga ukuthi (0,5 · Π-x) = -1. Manje sithola -Sin (x).
Ngakho, thatha esuselwe cosine, thina '= -Sin (x) I-y umsebenzi = Cos (x).

I esuselwe cosine yisikwele

Isibonelo Balisebenzisa isetshenziswa lapho esuselwe cosine. Umsebenzi y = Cos ² (x) eziyinkimbinkimbi. Sithola ngowokuqala amandla umehluko umsebenzi nge exponent 2, okungukuthi 2 · Cos (x), khona-ke iyanda yi esuselwe (Cos (x)) ', okuyinto -Sin alinganayo (x). Thola y '= -2 · Cos (x) · Sin (x). Lapho kusebenza Sin ifomula (2 · x), i-sine ye-engeli double, ukuthola Esenziwe Lula lokugcina
Ukusabela y '= -Sin (2 · x)

imisebenzi ephambene

Zifakwe ekutadisheni eyala eziningi lobuchwepheshe mathematics, isibonelo, ukwenza kube lula ukubala integrals, isixazululo of umehluko zibalo. Basuke uzwakalise ngokuya imisebenzi Trigonometric enokungqubuzana ngengqondo, ephambene ngakho cosine ch (x) = Cos (i · x) lapho i - kuyinto iyunithi ngengqondo, ephambene sine sh (x) = Sin (i · x).
i-hyperbolic cosine ibalwa nje.
Cabanga umsebenzi y ^{= (e x + e -X)} / 2, lena ephambene cosine ch (x). Ukusebenzisa umthetho lokuthola esuselwe isamba izinkulumo ezimbili, ukususwa ngokuvamile Okuphindaphinda njalo (const) ngoba isibonakaliso esuselwe. Igama elithi ka 0.5 yesibili · e ^-X - umsebenzi eziyinkimbinkimbi (esuselwe salo -0,5 · e ^-X), 0.5 · f ^x - eThemini. (Ch (x)) '= ((e ^x + e ^{- x)} / 2)' kungenziwa ebhaliwe ehlukile: (0.5 · e · ^x + 0.5 e ^{- x)} '= 0.5 · e ^x -0,5 · e ^{- x,} ngoba esuselwe (e ^{- x)} 'ilingana -1, ukuze umnnozhennaya e ^{- x.} Umphumela waba umehluko, futhi lena ephambene sh sine (x).
Isiphetho: (ch (x)) '= sh (x).
Rassmitrim isibonelo sendlela ukubala esuselwe umsebenzi y = ch (x ³ +1).
Ngu kwamangqamuzana umthetho i-hyperbolic cosine nge eziyinkimbinkimbi agumenti y '= sh (x ³ +1) · (x ³ +1)' lapho (x ³ + 1) = ³ · x ² + 0.
A: I-esuselwe kule umsebenzi ilingana 3 · x ² · sh (x ³ +1).

Izisetshenziswa ezilethwayo okuxoxwe imisebenzi y = ch (x) kanye no-y = Cos (x) ithebula

Ngesikhathi isinqumo sezibonelo akudingekile isikhathi ngasinye ukuhlukanisa kubo ku scheme ehlongozwayo, sebenzisa okukhipha ngokwanele.
Isibonelo. Ukuhlukanisa umsebenzi y = Cos (x) + Cos ² (-X) -Ch (5 · x).
Kulula ukubala (ukusetshenziswa labalwa idatha), y '= -Sin (x) + Sin (2 · x) -5 · Sh (x · 5).