Ko rite ki te whenu o te taua koki te pärönaki o te aho o te koki

Dana mahi pākoki ohie y = hara (x), he differentiable i ia wāhi o te rohe katoa. E ti'a ia tatou whakamatau e te pärönaki o te aho o tetahi tautohe he rite ki te whenu o te taua koki, e ko, '= Koha (x).

E hāngai ana te tohu kei runga i te auraa o te mahi pārōnaki

tautuhi tatou x (te noho) i roto i te tahi mau tata iti o te wāhi ngā x Δh _0. Ka whakaatu matou i te uara mahi i roto i taua mea, me i te wāhi x ki te kitea te nuku o te mahi i homai. Ki te Δh - incremented tautohe, te tautohe hou - tenei x ₀ + Δx = x, he rite te uara o tenei mahi mo te uara i homai o te tautohe (x) hara (x ₀ + Δx), te uara mahi i te wāhi motuhake (x ₀₎ he mōhiotia hoki .

Na to tatou Δu = hara (x ₀ + Δh) -Sin (x ₀₎ - whiwhi mahi nuku.

E ai ki te tātai o te moni sine o rua koki taurite ka tahuri tatou te rerekētanga Δu.

Δu = hara (x ₀₎ · Koha (Δh) + Koha (x ₀₎ · hara (Δx), haunga te hara (x ₀₎ = (Koha (Δx) -1 ) · hara ( x ₀₎ + Koha (x ₀₎ · hara (Δh).

ngā raupapa whakamana whakarōpū tuatahi ki te toru hara (x _0), tangohia atu te take noa - hara - nga taiapa. riro matou i roto i te faaiteraa Koha rerekētanga (Δh) -1. mahue te reira ki te huri i te tohu i roto i mua o te taiepa, me taiapa. E matau he aha te te 1-Koha (Δh), meinga matou te huringa me te whiwhi i te faaiteraa māmā Δu, ka e nei wehea e Δh.
ka whai Δu / Δh te puka: Koha (x ₀₎ · hara (Δh) / Δh 2 · hara ² (0.5 x Δh) · hara (x ₀₎ / Δh. Ko te ōwehenga o te nuku o te mahi ki te whakauru ki te nuku o te tautohe tenei.

tonu te reira ki te kitea te rohe o nga ōwehenga whiwhi e tatou i roto i Lim Δh, tiaki ki te te kore.

Kei te mohiotia te reira e te rohe o Hini (Δh) / he rite ki te 1 Δx, i raro i te huru. Na te faaiteraa 2 · hara ² (0.5 x Δh) / Δh i te moni ngā panoni hua ki te hua kei roto rite whakanui tuatahi rohe faahiahia: te taurunga o te hautau me te znemenatel wehenga i te 2, te tapawha o te aho whakakapi hua. Tenei te pehea:
(Hara (0,5 · Δx) / (0,5 · Δx)) · hara (Δx / 2).
Ka waiho i te rohe o tenei faaiteraa, ina whakapaia e Δh ki te kore, rite ki te maha o te kore (0 whakanuia e 1). Huri i te reira i roto i taua i te rohe o te ōwehenga Δy / Δh ko Koha (x ₀₎ · 1-0, ko tenei Koha (x _0), he motuhake o Δh te faaiteraa o e tiaki ki te 0. Ko te mutunga: ko te pärönaki o te aho o tetahi koki he rite ki te x whenu o x, e taea te tuhituhi rite: y '= Koha (x).

whakarārangitia te tātai hua i roto i te tepu o nga pärönaki mohiotia, te wahi i nga mahi timatanga katoa

I roto i te whakaoti rapanga, te wahi tutaki ia te pärönaki o te hara, ka taea e koe te whakamahi i te ture o te pārōnaki me tātai rite-hanga o te tepu. Hei tauira: kitea te pärönaki o te mahi māmā y = 3 · hara (x) -15. whakamahi tatou i te ture te takenga tango tauwehe tau timatanga mo te tohu o te pārōnaki me te tātai i te maha tonu pārōnaki (i te mea kore). Hoatu he uara tepu sine o te pärönaki o te koki x Koha rite (x). Kia riro te whakahoki: y '= 3 · Koha (x) -E. Tenei pārōnaki, i roto i te tahuri, he hoki he mahi y = H timatanga · Koha (x).

Ko te pärönaki o hara tapawha o tetahi tautohe

I roto i te tātaitanga o te faaiteraa (Hini ² (x)) 'Me mahara mahi pehea rerekëtanga matatini. Na, ² = hara (x) - ko te mahi mana rite aho tapawha. Ko hoki tōna tautohe te mahi pākoki, he tautohe matatini. Ko te hua i roto i tenei take, ko te rite ki te hua o te whakanui tuatahi ko te tapawha o te pärönaki matatini o te tautohe, me te tuarua - te pärönaki o te aho. Tenei te te ture mō te differentiating he mahi o te mahi: (u (v (x))) 'Kei te (u (v (x)))' · (v (x)) '. Expression o v (x) - he tautohe matatini (mahi ā-). Ki te te taumahi homai "y ōrite tapawha te aho x", ka ko y te pärönaki o tenei mahi hiato '= 2 · hara (x) · Koha (x). Ko te hua o te whakanui tuatahi rererua - pärönaki mohiotia mahi taup, ko Koha (x) - pakohu pärönaki tautohe matatini o te mahi pūrua. Ka taea e te hua whakamutunga kia puta ke, ara te whakamahi i te tātai o te aho pākoki o te koki rua. A: Ko te pārōnaki ko hara (2 · x). He ngāwari ki te mahara tenei tātai, Kei te maha whakamahia reira rite te tepu.