Sida derivative of saarka cosine ah

derivative ee cosine ay la mid tahay ku derivative of the Culumida saleysan caddeyn - qeexidda function xadka. Waxaa macquul ah in la isticmaalo hab kale oo la isticmaalayo qaaciidooyinka trigonometric wadida Culumida Soomaaliyeed iyo cosine xaglo. Fikraddaada hal shaqo oo kale ka dib - iyada oo a cosine Culumida, Culumida, iyo kala Xujo adag.

Ka fiirso tusaale ugu horraysay ee wax soo saarka ee caanaha (Koos (x))

Sii inremantiga dayac Δh muran x of y = Koos (x). Haddii qiimaha cusub ee Xujada x + Δh hesho qiimaha cusub Koos function (x + Δh). Markaas inremantiga function Δu noqon doonaa si siman u nimid Koos (x + Δx) -Cos (x).
Ratio of function inremantiga waxay noqon doontaa Δh noocan oo kale ah: (Koos (x + Δx) -Cos (x)) / Δh. Isku Aadka transformations aqoonsi keentay in sarreeyaha ee jajabka. Xasuustaan formula cosines farqiga, natiijadu waa -2Sin shaqada (Δh / 2) by Sin ku badiyey (x + Δh / 2). Waxaan ka heli xadka Lim alaabta this gaar ah by Δh markii Δh socotaa in eber. Waxaa la og yahay in marka hore (oo loo yaqaanno cajiib ah) xadka Lim ah (Sin (Δh / 2) / (Δh / 2)) waa loo siman yahay ilaa 1, iyo xaddido -Sin (x + Δh / 2) waa loo siman yahay -Sin (x) marka Δx, in lasugo in eber.
Waxaan ku qor natiijada: derivative ah (Koos (x)) waa - Sin (x).

Qaar ka mid ah door bidaan Habka labaad ee tobanaad formula la mid ah

ka tirignoomatari yaqaan: Koos (x) Waa isku mid Sin (0,5 · Π-x) Sidoo kale Sin (x) waa Koos (0,5 · Π-x). shaqo adag Markaas differentiable - Culumida Soomaaliyeed ee xagal dheeraad ah (halkii X cosine).
Waxaan aad u hesho Koos sheyga (0,5 · Π-x) · (0,5 · Π-x) ', maxaa yeelay, derivative of cosine ku Culumida Soomaaliyeed ee x waa x. Helitaanka caanaha labaad Sin (x) = Koos (0,5 · Π-x) bedelay cosine iyo Culumida ah, ogow in kuwa (0,5 · Π-x) = -1. Hadda waxaan ka heli -Sin (x).
Sidaas daraaddeed, qaadan derivative of cosine ah, aannu = -Sin (x) ee y shaqada = Koos (x).

derivative ee cosine afar gees

Tusaale A si joogto ah loo isticmaalo waxaa loo isticmaalaa meesha derivative of cosine ah. y Shaqada = Koos ² (x) adag. Waxaan ka heli function ugu horeysay ee awoodda kala duwan la jibbaarada 2, in uu yahay 2 · Koos (x), ka dibna waxa lagu dhufto derivative ah (Koos (x)), taas oo loo siman yahay -Sin (x). Soo hel y '= -2 · Koos (x) · Sin (x). Marka loo baahdo caanaha Sin (2 · x), Culumida Soomaaliyeed ee xagal double, heli fududeeyay finalka
jawaab y '= -Sin (2 · x)

hawlaha hyperbolic

Codsatay in ay daraasadda of nidaamo badan farsamo ee xisaabta, tusaale ahaan, ay u fududaato si ay u xisaabiso integrals, xal of isla'egyada kala duwan. Waxay waxaa ka muujiyay in marka la eego hawlaha trigonometric dood khayaali ah, ch cosine si hyperbolic (x) = Koos (i · x) halkaas oo i - Waa unug khayaali ah, sh Culumida hyperbolic (x) = Sin (i · x).
cosine Hyperbolic waxa loo xisaabinayaa si fudud.
Ka fikir shaqada y ^{= (e x + e -x)} ee / 2, tani waa ch ah cosine hyperbolic (x). Isticmaalka xukunka helo derivative ah wadarta labada tibaaxaha, ka saarida sida caadiga ah multiplier joogto ah (Const) ee calaamada derivative ah. Erayga labaad ee 0.5 · e ^-x - shaqo adag (oo ay derivative waa -0,5 · e ^-x), 0.5 · f ^x - muddo xileedka koowaad. (Ch (x)) = ((e ^x + e ^{- x)} / 2) "waxaa loo qori karaa si ka duwan: (0,5 · e · ^x + 0.5 e ^{- x)} = 0,5 · e ^x -0,5 · e ^{- x,} maxaa yeelay, derivative ah (e ^{- x)} waa loo siman yahay si -1, si umnnozhennaya e ^{- x.} Natiijada waxa ay aheyd kala duwan yihiin, oo tanuna waa sh ah hyperbolic Culumida Soomaaliyeed (x).
Gunaanad: (ch (x)) = sh (x).
Rassmitrim tusaale ka mid ah sida loo xisaabiyo derivative of function y = ch ah (x ³ +1).
By xukunka kala cosine hyperbolic leh adag y muran '= sh (x ³ +1) · (x ³ +1) halkaas (x ³ + 1) = 3 · x ² + 0.
A: derivative ee shaqada this waa loo siman yahay ilaa 3 · x ² · sh (x ³ +1).

Taagayo wada hadlay hawlaha = ch y (x) iyo y = Koos (x) miiska

At go'aanka tusaalooyin ah muhiim ma aha in mar kasta si ay u kala on nidaamka la soo jeediyay, isticmaalaan wax soo saarka ku filan.
Tusaale. Kala y shaqada = Koos (x) ee + Koos ² (-x) -Ch (5 · x).
Waa ay fududahay xisaabinta (isticmaalka xisaabaya data), y '= -Sin (x) + Sin (2 · x) -5 · Sh (x · 5).