Dérivés nhamba: pakuverenga nzira uye mienzaniso

Zvichida pfungwa rinobva inozivikanwa tose kubva chesekondari. Kazhinji vadzidzi vachinetseka kunzwisisa ichi urwu, zvinokosha chaizvo chinhu. Zvinonzi achishingaira kushandiswa munzvimbo dzakasiyana-siyana hwevanhu, uye vazhinji ouinjiniya vakanga yakavakirwa chaiyo iri masvomhu vakawana nokuda rinobva. Asi vasati mberi kuongorora chii rinobva nhamba sezvo ivo overenga uye apo Vachauya batsira, yokunyatsoongorora zvishoma kupinda kare.

nyaya

Pfungwa rinobva, ndiro hwaro kwemasvomhu pachisara akanga akazaruka (kunyange nani kutaura "kutanga" nokuti, yakadaro, hakuwaniki zvakasikwa) Isaakom Nyutonom, uyo isu tose kubva kuwanikwa nomurayiro regiravhiti. Ndiye wokutanga akashandisa pfungwa iyi wefizikisi nokuda kunyorerana hunhu kumhanya uye kumhanyisa miviri. Uye masayendisiti akawanda tichirumbidza Newton nokuda kwazvo kuvamba ichi, nekuti chokwadi iye akazogadzira hwaro differential uye chinokosha calculus, kuti ndeechokwadi hwaro yose munda wemasvomhu anonzi "kwemasvomhu kuongorora". Kana panguva Nobel Prize, Newton zvichida angadai kurigamuchira kakati.

Kwete pasina dzimwe pfungwa huru. Kuwedzera Newton pamusoro pokumuka rinobva uye chinokosha vakashanda inozvikudza geniuses wemasvomhu sezvo Leonhard Euler, Lagrange uye Louis Gotfrid Leybnits kwakadaro. Zviri kuvonga kwavari tine dzidziso differential calculus muchimiro nayo iripo nhasi. Sezvineiwo, ichi ndicho Leibniz vawana geometric zvinoreva rinobva, yaiva chinhu kupfuura yakatenuka tangent kusvikira girafu pakati mashandiro.

Chii rinobva nhamba? Ikakuruma wodzokorora zvakaitika muchikoro.

Chii rinobva?

Dudzira pfungwa iyi nenzira dzakasiyana. The nyore tsananguro: Dérivés - ndiwo mwero shanduko chaitika. Dzinomirira girafu upi kushanda ja ose x. Kana hazvina kururamiswa, ine zvimwe makakombama vari girafu, iyi nokuwedzera uye kuderera. Kana iwe tora chero kamwoyo penguva nepurogiramu, richava yakarurama mutsetse chidimbu. Saka, nhamba iri kukura ane kamwoyo chidimbu kubva ja kuti kukura X batanidza, uye achava rinobva pakati mashandiro pane imwe nguva. Kana tikafunga mashandiro rose, pane imwe nguva, tiri kuwana kushanda rinobva, kureva imwe pazviri X and.

Uyezve, kunze zvinoreva rinobva sechinhu Zvaiitwa mwero shanduko mumuviri, kunewo geometric pfungwa. Pairi tinokurukura ikozvino.

The geometric zvinoreva

Dérivés nhamba pachavo vari mumwe nhamba kuti haisi kunyatsonzwisisa haarambi chero zvaanoreva. Zvakaratidza kuti rinobva haasi chete inoratidza kukura mwero kana kuderera mashandiro, uye yakatenuka tangent kusvikira girafu pamusoro mashandiro panguva iyoyo. Kwete zvachose pachena tsananguro. Ngationgororei zvizere. Ngatitii tine girafu munhu basa (kutora mubereko munyonga). It ane magumo nhamba pfungwa, asi kune dzimwe nzvimbo uko chete chete pfungwa ane vaifanira kana mashoma. Kuburikidza chero pfungwa yakadaro, unogona kuswedera yakarurama mutsetse, iyo yaizova perpendicular kuti girafu pamusoro mashandiro panguva iyoyo. mutsetse uyu achanzi tangent. Ngatitii tiri yaiitika kusvikira mharadzano pamwe akabatana mombe. Saka yakawanikwa pakati tangent uye akabatana nzombe uye angled achazviisa nokuda rinobva. More zvakananga, zviri tangent wenyika angled ichi zvichava nahwo.

Ngatimbotaura zvishoma pamusoro zvimwe zviitiko uye nomukaka Ngationgororei nhamba.

Special zviitiko

Sezvataona kare ambotaurwa, nomukaka nhamba - rinobva ukoshi paneimwewo pfungwa. Pano, Somuenzaniso, tora mashandiro ja = X ^2. The rinobva kuna X - nhamba, asi vakawanda - rimwe basa akaenzana 2 * x. Kana tichida kuverenga rinobva Somuenzaniso, panguva X ₀ = 1, tinowana and '(1) = 2 * 1 = 2. Ndicho nyore chaizvo. An dzinonakidza nyaya ndiyo rinobva pamusoro zvakaoma nhamba. Kupinda uchida tsananguro chii kunzwisisa nhamba, hatisi. Zvakakwana kutaura kuti nhamba iri rine dzinonzi zvekufungidzira chikwata - nhamba ane pachivara vakaenzana -1. The kukarukureta kuti rinobva zvinokwanisika chete pasi zvinotevera ezvinhu:

1) Panofanira kuva wokutanga hurongwa rushoma nomukaka zviri zvechokwadi uye zvekufungidzira mativi ja uye X.

2) mamiriro ezvinhu enyika Cauchy-Riemann chokuita kuenzana zvishomanana anorondedzerwa mundima yokutanga.

Imwe nyaya dzinonakidza, kunyange sezvo kuoma sezvo yapfuura mumwe, rinobva zvakaipa nhamba. Kutaura zvazviri, chero uchinzwa nhamba zvinogona achimiririrwa yakanaka, kane -1. Eya, rinobva uye kugara basa akaenzana kugara vawanda kubudikidza rinobva pakati mashandiro.

Zvichava kuziva nezvebasa nomukaka muupenyu hwavo hwezuva nezuva, uye ichi ndicho ikozvino tokurukura nezvacho.

kunyoresa

Zvichida mumwe nomumwe wedu kanenge kamwe hwose ndinoerekana ndava kufunga kuti masvomhu angangotadza kubatsira kwaari. Neyokuti yakaoma chinhu sezvo rinobva zvimwe haana kushandisa. Kutaura zvazviri, vaBhasemati - inokosha nesayenzi, uye zvose zvibereko anova kunyanya wefizikisi, kemisitiri, zvenyeredzi uye kunyange upfumi. Rinobva chakaratidza kutanga kwemasvomhu pachisara iyo akatipa mukana vafunga kubva calculators mitambo, uye takadzidza kududzira mitemo yezvinhu zvakasikwa uye kutendeuka kuti zvakavanakira nokuda kwayo.

mhedziso

Chokwadi, haasi munhu wose anogona kubatsira kuti rinobva muupenyu chaihwo. Asi pamasvomhu anovandudza pfungwa zvirokwazvo kuti achada. Pasina nokuti masvomhu anonzi mambokadzi sayenzi: nayo ine nzwisiso vamwe minda zivo.