E like me ka derivative o ka cosine ia auoiaea

Ke derivative o ka cosine mea i 'ano like me ka derivative o ka sine muli o ka hoike - ka wehewehena o ke kuleana pili i kona palena. He hiki ke hoʻohana i kekahi papa hana ka hoʻohana trigonometric nā papakuhikuhi no e hoohauhee ana i ka sine a me ka cosine pana pua. Ka hoike i kekahi hana ma hope o kekahi - ma ka sine cosine, sine, a differentiate me ka luna 'loulou.

ke kumu mua o ka auoiaea o ka haʻilula noonoo (Cos (m)) '

E haawi negligible xi Δh hoʻopaʻapaʻa m ka y me = Cos (m). Inā ka hou cia o ka manaʻo hoʻopiʻi kū'ē m + Δh loaa i ka hou cia Cos kuleana pili i (m + Δh). A laila, xi Δu hana e e like no Cos (m + Δx) -Cos (m).
Ka lākiō o ka papa xi e e ia he Δh: (Cos (m + Δx) -Cos (m)) / Δh. E unuhi oe i wahine paha, loli 'kūpono ma ka numerator o ka mahele. Ke hoole i haʻilula koena unuhi cosines, i ka hopena o ka hana -2Sin (Δh / 2) hoonuiia e Sina (m + Δh / 2). Mākou i loaʻa i ke kali Lim a pilikino ia huahana ma Δh ia Δh mālama i ka 'Aʻohe. Ua ua ike ia i ka mua (kapaia kamahaʻo) kali Lim (Sina lakou i hele (Δh / 2) / (Δh / 2)) mea like i 1, a kali -Sin (m + Δh / 2) ua like -Sin (m) ka wā Δx, hoʻolaha i 'Aʻohe.
E kākau i ka hopena: ka derivative (Cos (m)) 'mea - Sina lakou i hele (m).

Kekahi makemake i ka lua o ka hana o Napuelua ka ia haʻilula

Ua ikeia mai ka trigonometry: Cos (m) mea like Sina lakou i hele (0,5 · Π-m) like me Sina lakou i hele (m) o Cos (0,5 · Π-m). A laila, differentiable eiiieaena papa - ka sine o ka hou huina (kahi X cosine).
E loaa i ka huahana Cos (0,5 · Π-m) · (0,5 · Π-m) ', no ka mea, o ka derivative o ka sine cosine o ka m ka m. Ka loaʻa'an i ka lua o ka haʻilula Sina lakou i hele (x) = Cos (0,5 · Π-m) ke kūapoʻana i ka cosine, a me ka sine, noonoo i (0,5 · Π-m) = -1. Ano, e hele mākou -Sin (m).
No laila, lawe i ka derivative o ka cosine, ua '= -Sin (m) no ka papa y me = Cos (m).

Ke derivative o cosine hana huinahā

A pinepine hoʻohana laʻana ua hoʻohana 'ia ma kahi o ka derivative o ka cosine. Ka papa y me = Cos ² (m) eiiieaena. Mākou i loaʻa ka mea mua palena pau ka mana hana me ka exponent 2, i mea 2 · Cos (m), a laila ka mea, ua hoonuiia e ka derivative (Cos (m)) ', i mea like -Sin (m). Loaa y me '= -2 · Cos (m) · Sina lakou i hele (m). I ka pili Sina lakou i hele haʻilula (2 · m), i ka sine o ka waʻa huina, loaa i ka hope loa Nohie
muli o y me '= -Sin (2 · m)

hyperbolic oihana

Pili a hiki i ka hoʻopaʻa 'ana o na mea he nui oaoieei-ka hoʻopaʻi' ana ma ka makemakika, no kekahi laʻana, e ka mea maʻalahi e hoʻomaulia integrals, pāʻoihana o ka palena pau nā helu kaulike. Ka mea, i kāheaʻia ma ka hua'ōlelo o trigonometric oihana a me ka mana ae kekahi manaʻo hoʻopiʻi kū'ē, no laila, hyperbolic cosine Ch (x) = Cos (au · m) kahi aʻu - mea he mana pa alima, hyperbolic sine sh (x) = Sina lakou i hele (au · m).
Hyperbolic cosine he pōpilikia wale.
E noonoo oe i ka papa y me ^{= (e m + E -x)} / 2, keia mea i ka hyperbolic cosine Ch (m). E ho ohana i ka noho aliʻi o ka loaa ia makou kekahi derivative i ka huina o ka elua, ka 'aoʻao, ka wehe' ia 'ana eia i multiplier (Const) no ka hoailona o ka derivative. I ka lua o ka manawa o ka 0.5 · E ^-x - luna 'kuleana pili i (kona derivative mea -0,5 · E ^-x), 0.5 · [illegible] ^m - ka mua makahiki. (Ch (m)) '= ((e ^m + e ^{- m)} / 2)' hiki ke kākau okoa: (0,5 · E · ^m + 0.5 e ^{- m)} '= 0,5 · e ka ^m -0,5 · e ^{- m,} no ka mea, o ka derivative (e ^{- m)} 'ua like ia -1, e umnnozhennaya e ^{- m.} Ka hopena ua i ka oko ao, a me keia mea i ka hyperbolic sine sh (m).
Ka Hopena: (Ch (m)) '= sh (m).
Rassmitrim i laʻana o ana, e hoʻomaulia i ka derivative o ka papa y me = Ch (m ³ +1).
By differentiation rula hyperbolic cosine me ka luna 'i kekahi manaʻo hoʻopiʻi y me' = sh (m ³ +1) · (m ³ +1) 'kahi (m ³ + 1) = 3 · m ² + 0.
A: ka derivative o keia kuleana pili i ka like i 3 · m ² · sh (m ³ +1).

Nā mea loaʻa kūkā oihana y me = Ch (m) a me y me = Cos (m) papaʻaina

Ma ka olelo hooholo o na examples mea i pono kēlā me kēia manawa, e differentiate ia ma luna o ka mea i manaoia noaia, e hoʻohana i ka auoiaea lawa.
Laʻana. Differentiate i ka papa y me = Cos (m) + Cos ² (-x) -Ch (5 · m).
He oluolu ke compute (hoʻohana tabulatedʻikepili), y me '= -Sin (m) + Sina lakou i hele (2 · m) -5 · Sh (m · 5).