Imithetho esisiseko lweemeko ezahluka-hlukeneyo, isicelo izibalo

Okokuqala, kubalulekile ukukhumbula ukuba umahluko loo kunye nentsingiselo mathematical leentyatyambo.

umsebenzi umahluko ke imveliso komsebenzi yemvelaphi le ngxoxo phezu umahluko we ingxabano. Ngokwezibalo, le ngcamango angabhalwa yokubonisa: dy = y '* DX.

Naye, ukuba ukujonga yemvelaphi ye y yokulingana '= lim DX-0 (dy / DX), yaye zijongisise umda - i-dy ibinzana / DX = x' + α, apho α parameter nobungakanani omncane zezibalo.

Ngoko ke, omabini amacala binzana kufuneka iphindaphindwe DX, nto leyo ekugqibeleni unika dy = y '* DX + α * DX, apho DX - yinto utshintsho omncane kwi benixambulisana, (α * DX) - ixabiso apho nokungahoywa, ngoko Dy - anyuswe imisebenzi, kunye (y * DX) - kwindawo engundoqo ye ukwenyuselwa okanye umehluko.

umsebenzi umahluko ke imveliso komsebenzi livela kwi umahluko we ingxabano.

Ngoku kuyimfuneko ukuba siqwalasele imigaqo esisiseko lweemeko ezahluka-hlukeneyo, adla ngokusetyenziswa uhlalutyo zezibalo.

Theorem. imali uvumelane elingana sum of imveliso ezifunyenwe amacandelo: (a + c) = a '+ c'.

Ngokufanayo, lo mgaqo kuya kuba okusebenzayo yemvelaphi umahluko.
Neziphumo danogo imithetho umahluko kukuba Kuluvo ukuba yemvelaphi eziliqela ukulingana ukuya sum of kweemveliso ezifunyenwe yi la magama.

Ngokomzekelo, xa ufuna ukufumana yemvelaphi elithi (a c-k +) ', ngoko ke Isiphumo ukubonakaliswa' + c 'k'.

Theorem. Imveliso eminye imisebenzi zezibalo differentiable kwindawo elilingana sum eyenziwa imveliso into yokuqala ukuya yemvelaphi yesibini kunye nemveliso into yesibini ukuya ithe kuqala.

Theorem elichazwa ngokwezibalo ngokuba kubhaliwe kwathiwa ngolu hlobo lulandelayo: (a * c) '= i * i' + a 's. Iziphumo theorem kukupheliswa ukuba into rhoqo kwi yemvelaphi imveliso isiwe ngaphandle umsebenzi esukela.

Xa ngendlela yokubonisa aljibra, lo mthetho ibhalwe ngolu hlobo lulandelayo: (a * c) = a * a ', apho kukho = nengngqi.

Ngokomzekelo, xa ufuna ukufumana yemvelaphi ibinzana (2a3) ', umphumo uba impendulo: 2 * (A3) = 2 * 3 * 6 * A2 = A2.

Theorem. imisebenzi ubuhlobo nesimo elingana umlinganiselo phakathi umahluko yemvelaphi elingezantsi liphindaphindwe elingezantsi kunye amaxesha kwinani le yemvelaphi elingezantsi kunye isikweri elingezantsi.

Theorem elichazwa ngokwezibalo ngokuba kubhaliwe kwathiwa ngolu hlobo lulandelayo: (a / c) '= ( a' * ibe * i-c ') / ^2.

Xa ndiqukumbela, kuyimfuneko ukuba siqwalasele ulawulo ngenxa umehluko imisebenzi ahlanganisiweyo.

Theorem. Banikwa fuktsii y = f (x), apho x = c (t), ngoko ke umsebenzi y, ngokumalunga t-bume, ebizwa ngokuba complex.

Ngenxa yoko, kuzo phaya kuhlalutyo nokungokwezibalo yemvelaphi umsebenzi edityanisiweyo ithathwa njenge yemvelaphi umsebenzi liphindaphindwe yemvelaphi sub-imisebenzi yayo. Kuba lula kwemithetho umahluko kwemisebenzi entsonkothileyo kakhulu ngokohlobo itafile.

Kunye nokusetyenziswa rhoqo le theyibhile kulula ukukhumbula yezabelo. Ezinye yezabelo kwemisebenzi ezinzima inokufumaneka, ukuba sisebenzisa imithetho umahluko lwemisebenzi ziye ezibekwe theorems kunye corollaries kubo.