Usekela uhlalutyo yezibalo. Njani ukufumana le ithe?

Yemvelaphi umsebenzi f (x) kwi umsebenzi kwindawo x0 ethile ebizwa ratio ukukhula umda ukuya ukwenyuselwa Kwempikiswano, ngokuxhomekeka ekubeni x ukuba 0, kwaye umda ikhona. Uvumelane ngokubanzi elijongene stroke, maxa wambi nge ingongoma okanye nge umahluko. Ngokufuthi, le yemvelaphi ezintlanganweni umda iziphumo ezilahlekisayo, ekubeni umelo eso sisetyenziselwa enqabile.

Umsebenzi, eba yemvelaphi kwindawo x0 othile, ebizwa differentiable kwindawo enjalo. Zicingele, D1 - ezininzi kuThixo lamanqaku apho umsebenzi f liza kwahlulwa. Anike ngamnye omnye amanani x, endingowakhe D f '(x), siye sifumane uphawulo indawo umsebenzi D1. Lo msebenzi yemvelaphi y = f (x). Yonyulwa: f '(x).

Ngaphezu koko, lo ithe ezisetyenziswa physics kanye zobunjineli. Cinga umzekelo olula. Oshukunyiswa Indawo eziphathekayo kwi ukulungelelanisa axis, xa ebuzwa ukuba umthetho sesindululo, oko kukuthi, x-Inanai elihambiselanayo lika le ngongoma yaziwa x (t) function. Ngeli xesha lekhefu ukusuka t0 ukuya t0 + t lilingana ukubana lwendawo x (t0 + t) -x (t0) = x, nesantya ngokomlinganiselo v (t) ulingana no'x '/ t.

Ngamanye amaxesha uhlobo isindululo thaca ukuze ngesantya ayitshintshi ngamakhefu kwixesha encinane, nto leyo ethetha ukuba intshukumo kunye iqondo elikhulu okuchaneka kuthathwa ukuba zifane. Kungenjalo, ukuba ixabiso le-avareji isantya ukuba t0 lulandelayo ukuba ixabiso ethile ngqo ngokupheleleyo, yaye ubizwa ngokuba isantya lwephanyazo v (t0) ukuba indawo ngexesha elithile t0. Kukholelwa ukuba kwisantya lwephanyazo v (t) yaziwa nawuphi na umsebenzi x ngokwahlukeneyo (t), ingaba v (t) ulingana no'x '(t). Ngamafutshane, isantya - yinto yemvelaphi uququzelelo ixesha.

Velocity leso unemilinganiselo kuzo ebezintle nezo zingentle, kwaye ixabiso le-0 Ukuba ngexesha lekhefu ethile (T1; T2) yi-HIV, ngoko uhamba indawo kwicala elinye, ngamanye amazwi, x (t) nokulungelelanisa ukunyuka nge ixesha, kwaye ukuba v (t) lelikhabayo, ngoko ke ukunxibelelanisa x (t) kunciphisa.

Kwiimeko ezimbaxa ngakumbi, ingongoma edakasa-moya okanye indawo. Ke Velocity ka - wobungakanani yomzobo, kwaye imisela ngamnye uququzelelo ye eya kumda wesangqa v (t).

Ngokufanayo, umntu akwazi ukuthelekisa yokunyusa ngongoma. Isantya umsebenzi ixesha, oko kukuthi, v = v (t). A livela loo msebenzi - isindululo lunikezelo: a = V '(t). Oko kukuthi, ukuba ujika ukuba ixesha yemvelaphi isantya lunikezelo.

Masithi y = f (x) - nawuphi na umsebenzi ngokwahlukeneyo. Emva koko ke siqwalasele isindululo yencopho phezu ukulungelelanisa esiqwini, nto leyo ethatha indawo umthetho x = f (t). ulondolozo Mechanical ye yemvelaphi unika ithuba ukunika intsingiselo ecacileyo theorems le calculus umahluko.

Njani ukufumana le ithe? Ukufumana yemvelaphi komsebenzi kuthiwa umahluko yayo.

Beka imizekelo kwakho ukufumana indlela yemvelaphi umsebenzi:

Le livela msebenzi rhoqo elingana zero; yemvelaphi umsebenzi y = x 'ulingana kumanyano.

Nendlela yokufumana ngayo yemvelaphi iqhezu? Ukuze wenze oku, cinga la maxwebhu alandelayo:

Kuba naliphi x0 <> 0 esinalo

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

Kukho eminye imithetho, ukufumana indlela ithe. ezizezi:

Ukuba imisebenzi A and B umahluko indawo x0, ngoko mali yabo umahluko kwindawo: (A + B) '= A' + B '. Ngamafutshane, le yemvelaphi isixa esilingana ukuya sum of yezabelo. Ukuba umsebenzi neenkalo ngaxa lithile, ngoko ke kufuneka bendinokunyusa ku nothi xa silandela ingxabano kunothi inzuzo.

Ukuba imisebenzi A and B umahluko indawo x0, ngoko imveliso yabo umahluko kwi: (A * B) '= A'B + AB'. (Imisebenzi Iimfundiso kunye nezakhi zawo zibalwa xa x0 kuyo). Ukuba umsebenzi A (x) liza kwahlulwa e point x0, no C - rhoqo, ngoko CA umsebenzi neenkalo ngeli xesha kwaye (CA) '= CA'. Oko kukuthi, a rhoqo kuthathwe ngaphandle komqondiso ithe factor.

Ukuba imisebenzi A and B umahluko indawo x0, kwaye umsebenzi B akalingani zero, ngoko umlinganiselo kwabo umahluko kwi: (A / B) = (A'B-AB ') / B * B.