Bases izingabunjalo. Indlela yokuthola esuselwe?

Esuselwe a f umsebenzi (x) e ebangeni elithile x0 umsebenzi ngokuthi ukukhula isilinganiso awapheli anyuswe lwempikiswano, inqobo x ukuba 0, futhi umngcele ukhona. Esuselwe ngokuvamile esiqokiwe unhlangothi, ngezinye izikhathi nge iphuzu noma nge umehluko. Ngokuvamile, esuselwe cross-border edukisayo imiphumela, njengoba ukumelwa okunjalo kuyaqabukela asetshenziswa.

Umsebenzi, okuyinto ine esuselwe endaweni ethile iphuzu x0, ngokuthi differentiable weyesi ezinjalo. Lokucabanga, D1 - sebuningini amaphuzu lapho f umsebenzi umahluko. Ukwabela ngamunye eyodwa yezinombolo x, okuqondene D f '(x), sithola umsebenzi isiqu endaweni D1. Lokhu kusebenza esuselwe y = f (x). Ingabe eyabizwa ngokuthi: f '(x).

Ngaphezu kwalokho, i-esuselwe evame ukusetshenziswa yemvelo noma kwezobunjiniyela. Cabangela isibonelo esilula. Indaba iphuzu uhamba phezu Ukudidiyela-eksisi, lapho uJesu ebuzwa ukuthi yimuphi umthetho motion, ukuthi, x-Ukudidiyela leliphuzu is x (t) umsebenzi ezaziwayo. Phakathi isikhawu kusuka t0 ukuba t0 + t lilingana displacement we x iphuzu (t0 + t) -X (t0) = x, nesivinini v kwesilinganiso sayo (t) elilingana x / t.

Ngezinye izikhathi ubunjalo ezinyakazayo ethulwa ukuze ngesivinini esingamakhilomitha ayishintshi ngezikhawu encane sikhathi, okusho ukuthi ukunyakaza ngezinga enkulu ukunemba ubhekwa iyunifomu. Kungenjalo, ukubaluleka isilinganiso ijubane uma t0 kulandela ukuba inani elithile ngokuphelele enembile, futhi ubizwa ngokuthi i-v isivinini leso (t0) ukuthi iphuzu ngesikhathi esithile t0. Kukholakala ukuthi v isivinini leso (t) is nganoma yisiphi umahluko umsebenzi x (t), ngasiphi v (t) eyaziwa ilingana x '(t). Uma sikubeka kalula, isivinini - kuba esuselwe izixhumanisi isikhathi.

Isivinini leso inamanani okuhle nokubi, futhi ukubaluleka kuyinto 0. Uma kuwukuthi ngesikhathi esithile isikhawu (T1; t2) uthambekele kokuhle, bese uhamba iphuzu luhamba luye ohlangothini olulodwa, ngamanye amazwi, x (t) ukuxhumanisa kwanda isikhathi, futhi uma v (t) alivumi, ke Ukudidiyela x (t) incipha.

Ngo ngaphezulu Ezimweni eziyinkimbinkimbi, iphuzu siya indiza noma emkhathini. Khona-ke velocity we - eliningi vector, futhi inquma ngamunye izixhumanisi a v Vector (t).

Ngokufanayo, umuntu ungakwazi ukuqhathanisa ukusheshisa iphuzu. Speed umsebenzi isikhathi, okungukuthi, v = v (t). A esuselwe umsebenzi onjalo - ezinyakazayo ukusheshisa: a = v '(t). Okungukuthi, kuvela ukuthi esuselwe isikhathi speed ukushesha.

Ake sithi y = f (x) - yimuphi umsebenzi umahluko. Khona-ke singacabangela motion iphuzu kwi Ukudidiyela-eksisi, ebanjwa ngoba umthetho x = f (t). yesondlo Mechanical we esuselwe kunikeza ithuba ukunikeza incazelo ecacile theorems -calculus umehluko.

Indlela yokuthola esuselwe? Ukuthola esuselwe yomsebenzi libizwa kwamangqamuzana yayo.

Beka izibonelo zakho kanjani ukuthola esuselwe umsebenzi:

I esuselwe umsebenzi njalo ilingane no-zero; esuselwe y umsebenzi = x ilingana indlela eya ebunyeni.

Futhi indlela yokuthola esuselwe ingxenyenamba? Ukuze wenze lokhu, cabangela izinto ezilandelayo:

Ngoba noma yisiphi x0 <> 0 esinalo

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

Kukhona ezinye imithetho, indlela yokuthola esuselwe. okungukuthi:

Uma imisebenzi A no B umahluko iphuzu x0 ke isamba yabo umahluko weyesi: (A + B) '= A' + B '. Uma sikubeka kalula, esuselwe isamba ilingana nenani lezinombolo of the nemikhiqizo. Uma umsebenzi umahluko esikhathini esithile, khona-ke kumelwe ekwenyusweni zero uma kulandela ingxabano zero inzuzo.

Uma imisebenzi A no B umahluko iphuzu x0 ke umkhiqizo sabo umahluko ku: (A * B) '= A'B + AB'. (Amanani imisebenzi nemikhiqizo yabo kubalwa ngesikhathi x0 iphuzu). Uma umsebenzi A (x) is umahluko embonweni x0, futhi C - njalo ke CA umsebenzi umahluko Kuleli qophelo, (CA) '= CA'. Okungukuthi, isici njalo asikhiphele ngaphandle isibonakaliso esuselwe.

Uma imisebenzi A no B umahluko iphuzu x0, futhi umsebenzi B akulingani zero ke isilinganiso sabo futhi umahluko ku: (A / B) '= (A'B-AB') / B * B.