Turanga tātari pāngarau. Me pēhea te ki te kitea e te pārōnaki?

Pärönaki o te f pānga (x) i te rohe i huaina ōwehenga tupu motuhake mahi wāhi x0 ki te nuku o te tautohe, ngā taua x ki kia 0, ka vai te rohe. Pārōnaki tikanga whakaritea patu, i ētahi wā mā ira ranei mā te pārōnaki. E mea pinepine, te pärönaki o te ripeka-rohe hua tinihanga, mai te uaua whakamahia he kanohi taua.

Taumahi, e kua te pārōnaki i te x0 ngā wāhi, ka karanga differentiable i te wāhi taua. Me kī, D1 - he plurality o ngā i i rerekëtanga te mahi f te. Vahe ki ia tetahi o nga tau x, no D f '(x), whiwhi tatou te rohe ti'araa mahi D1. He pärönaki o y = f (x) tenei mahi. Kei te whakaritea rite: f '(x).

I tua atu, ko te pārōnaki nuitia whakamahia i roto i te ahupūngao me te engineering. Fakakaukau angé ki he fa'ifa'itaki'anga ohie. Ko te nuku mata rauemi i runga i te tuaka fakafekau'aki, ka ui ki ta te ture o te nekehanga, e te,-taunga x o tenei ira mohiotia te x (t) mahi. I roto i te wa wā i t0 ki t0 + t ōrite te displacement o te pūwāhi x (t0 + t) -x (t0) = x, me tona v tere toharite (t) rite ki te x / t.

I te tahi taime ki te āhua o te nekehanga aroaro kia e kore e te tere toharite huri i wā wa iti, te tikanga e whakaaro kaupapa ki te tohu nui o te tika e kia ōrite. Tērā, te uara o te toharite tere ki te whai t0 ki etahi uara tino pau, ka ko tuku ki rite te v tere inamata (t0) e wāhi i te kau ngā o te wā t0. Kei te whakapono te reira e mohiotia te v tere inamata (t) te mo tetahi mahi x rerekëtanga (t), i te mea v (t) he rite ki te x '(t). Mämä noa iho, te tere - ko reira he pärönaki o nga taunga o te wā.

He tere inamata uara e rua pai, me te kino, me te uara, ko te 0. ki te he te reira i te tetahi wā wa (T1: t2) he pai, na te nuku mata i roto i te ahunga taua, i.e., x (t) ruruku piki ki te wā, me te mea v (t) he tōraro, na te taururuku x (t) heke.

I roto i te atu take matatini, neke te wāhi i roto i te manureva ranei i roto i te wāhi. Na te tere o - te rahinga pere, me whakatau i ia o nga taunga o te v pere (t).

Waihoki, ka taea e tetahi whakataurite i te whakaterenga o te pūwāhi. Tere ko te mahi o te wā, arā, v = v (t). He pärönaki o taua te mahi - nekehanga whakaterenga: he = v '(t). E ko, huri i te reira i roto i taua i te pārōnaki wa o te tere ko te whakateretanga.

Pea y = f (x) - tetahi mahi rerekëtanga. Na ka taea e tatou whakaaro te nekehanga o te pūwāhi i runga i te tuaka fakafekau'aki, e tango wahi mo te ture x = f (t). tiaki pūkaha o te pārōnaki homai te whai wāhi ki te whakarato i te mārama tikanga o nga theorems o te tuanaki pārōnaki.

Me pēhea te ki te kitea e te pārōnaki? Te kimi i te pārōnaki i huaina o te mahi te tona pārōnaki.

A tuu i to koutou tauira o te āhua o ki te kitea te pärönaki o te mahi:

Ko te pärönaki o te mahi tonu rite ki te kore; He rite ki te kotahitanga pärönaki o te pānga y = x.

A me pehea ki te kitea te pärönaki o te hautanga? Ki te mahi i tenei, whakaaro te rauemi e whai ake nei:

Hoki tetahi ko x0 <> 0 to tatou

y / x = -1 / x0 * (x + x)

He etahi ture, me pehea ki te kitea te pārōnaki. ara:

Ki te te te mahi, me te B e x0 wāhi rerekëtanga, ka rerekëtanga ratou moni kei te i te pūwāhi: (A + B) '= A' + B '. Mämä noa iho, te pārōnaki o te moni e rite ana ki te moni o te pärönaki. Ki te rerekëtanga te mahi kei te i etahi wāhi, ka me nuku te reira ki te kore, no te whai i te tautohe ki te kore taonga.

Ki te te te mahi, me te B e x0 wāhi rerekëtanga, ka rerekëtanga ratou hua i: (He * B) '= A'B + AB'. (E tatau Uara mahi me o ratou pärönaki i te x0 pūwāhi). Ki te rerekëtanga te mahi A (x) kei roto i te wāhi ko x0, ko C - tamau, ka rerekëtanga CA mahi kei i tenei wāhi, me te (CA) '= CA'. Ko, he take tonu i tangohia i waho te tohu o te pārōnaki.

Ki te te te mahi, me te B e x0 wāhi rerekëtanga, a kahore he rite ki te kore te mahi B, ka rerekëtanga ano ratou ōwehenga i: (A / B) '= (A'B-AB') / B * B.