Ka rite ki te pärönaki o te putanga whenu

Ko te pärönaki o te whenu he rite ki te pärönaki o te aho pūtake o te taunakitanga - whakamāramatanga o te mahi rohe. Ko taea ki te whakamahi i tētahi atu tikanga te whakamahi i tātai pākoki mō te taraiwa i te aho me te whenu koki. A faaite i tetahi mahi i muri i tetahi - i roto i te whenu sine, hara, a ka rerekëtanga ki ki tautohe matatini.

A feruri i te hi'oraa tuatahi o te putanga o te tātai (Koha (x)) '

Homai hokiate nuku Δh tautohe x o Koha y = (x). Ki te te uara hou o te tautohe x + Δh whiwhi i te uara hou Koha mahi (x + Δh). Na ka nuku ka kia rite ki Koha Δu mahi (x + Δx) -Cos (x).
Ko te ōwehenga o te mahi nuku ka waiho he Δh taua: (Koha (x + Δx) -Cos (x)) / Δh. Te utu panoni tuakiri hua i roto i te taurunga o te hautau. Auporo tātai cosine rerekētanga, te hua ko te -2Sin mahi (Δh / 2) whakanuia e hara (x + Δh / 2). kitea e matou i te rohe Lim tūmataiti tenei hua e Δh ina whakapaia e Δh ki te kore. Kei te mohiotia te reira e te tuatahi (i huaina faahiahia) rohe Lim (hara (Δh / 2) / (Δh / 2)) he rite ki te 1, ka whakawhāiti -Sin (x + Δh / 2) Kei te rite -Sin (x) ka Δx, tiaki ki kore.
tuhituhi matou i te hua: te pārōnaki (Koha (x)) 'Ko - hara (x).

Ētahi hiahia te tikanga tuarua o te kimi i te tātai taua

Kia mohiotia i pākoki: Koha (x) he rite te hara (0,5 · Π-x) atoa hara (x) ko Koha (0,5 · Π-x). mahi matatini Na differentiable - te aho o te koki atu (hei utu X whenu).
whiwhi tatou i nga Koha hua (0,5 · Π-x) · (0,5 · Π-x) ', no te mea ko te pärönaki o te whenu aho o te x x. Te whakauru i te tātai tuarua hara (x) = Koha (0,5 · Π-x) whakakapi i te whenu, me te hara, whakaaro e (0,5 · Π-x) = -1. Na whiwhi tatou -Sin (x).
Na, tangohia te pärönaki o te whenu, 'tatou = -Sin (x) mō te pānga y = Koha (x).

tapawha te pārōnaki o whenu

whakamahia te tauira pinepine whakamahia te wahi te pärönaki o te whenu. Te pānga y = Koha ² (x) matatini. kitea e matou i te mahi pārōnaki te mana tuatahi ki te taupū 2, e ko te 2 · Koha (x), ka e whakanuia ai e te pārōnaki (Koha (x)) ', i te mea rite -Sin (x). Whiwhi y '= -2 · Koha (x) · hara (x). A, no te hāngai tātai hara (2 · x), te aho o te koki rua, whiwhi i te Ngāwari whakamutunga
whakautu y '= -Sin (2 · x)

mahi pūwerewere

Tono ki te ako o maha pekanga hangarau i roto i te pāngarau, hei tauira, kia māmā ake ki te tātai pāwhaitua, otinga o ngā whārite pārōnaki. E whakahuatia ratou i roto i ngā o ngā pānga pākoki ki tohenga pohewa, na pūwerewere ch whenu (x) = Koha (i · x) kei hea i - ko te wae pohewa, pūwerewere sh hara (x) = hara (i · x).
tātai pūwerewere whenu te noa.
A feruri i te pānga y ^{= (e x + e -x)} / 2, ko te ch pūwerewere whenu tenei (x). Mā te whakamahi i te ture o te kimi i te pärönaki te moni o rua kīanga, te tango te tikanga whakanui tonu (Const) mo te tohu o te pārōnaki. Ko te wā tuarua o 0.5 · e ^-x - mahi matatini (tona pärönaki ko -0,5 · e ^-x), 0.5 · f ^x - te wā tuatahi. (Ch (x)) '= ((e ^x + e ^{- x)} / 2)' e taea te tuhituhi rerekē: (0,5 · e · ^x + 0.5 e ^{- x)} '= 0,5 · e ^x -0,5 · e ^{- x,} no te mea te pārōnaki (e ^{- x)} 'he rite ki te -1, ki umnnozhennaya e ^{- x.} Ko te hua ko te rerekētanga, ka ko te sh aho pūwerewere (x) tenei.
Conclusion: (ch (x)) '= sh (x).
Rassmitrim he tauira o te āhua o ki te tātai i te pärönaki o te pānga y = ch (x ³ +1).
Na roto i te pārōnaki ture pūwerewere whenu ki matatini tautohe y '= sh (x ³ +1) · (x ³ +1)' te wahi (x ³ + 1) = 3 · x ² + 0.
He rite ki te 3 te pärönaki o tenei mahi · x ² · sh (x ³ +1): A.

kōrero pärönaki mahi y = ch (x) me te y = Koha (x) ripanga

I te whakatau o nga tauira e kore he e tika ana i ia wa ki te rerekëtanga ki a ratou i runga i te kaupapa e whakaarohia ana, te whakamahi i te putanga nui.
Tauira. Rerekëtanga ki te pānga y = Koha (x) + Koha ² (-x) -Ch (5 · x).
Ko reira ngāwari ki te whakatatau (te whakamahi raraunga ngä), y '= -Sin (x) + hara (2 · x) -5 · Sh (x · 5).