Imithetho eyisisekelo yokuzihlukanisa kwamangqamuzana ngokwemisebenzi yawo, isicelo wezibalo

Ukuze uqale, kuyafaneleka ukukhumbula ukuthi umehluko onjalo futhi incazelo zezibalo nalo.

umsebenzi Ukwahlukaniswa iwumkhiqizo umsebenzi esuselwe agumenti phezu umehluko agumenti. Izibalo, lo mqondo singatlolwa bunjesi isisho: dy = y '* dx.

Ngakwelinye ihlangothi, ukucacisa esuselwe y ukulingana '= lim dx-0 (dy / dx), futhi ukuthola ukuthi umkhawulo - the dy Inkulumo / dx = x' + α, lapho α ipharamitha kuncane ubuningi zezibalo.

Ngakho-ke, zombili okuvela kuyo le nkulumo kumele iphindwe dx okwagcina unika dy = y '* dx + α * dx, lapho dx - kuyinto ushintsho kuncane e-agumenti, (α * dx) - ukubaluleka okungase dengwane, bese dy - Isengezo imisebenzi, kanye (y * dx) - engxenyeni eyinhloko ye-anyuswe noma umehluko.

umsebenzi Ukwahlukaniswa iwumkhiqizo umsebenzi esuselwe phezu umehluko agumenti.

Manje-ke kubalulekile ukucabangela imithetho eyisisekelo yokuzihlukanisa kwamangqamuzana ngokwemisebenzi yawo, okuyinto avame ukusetshenziswa lapho kwenziwa izingabunjalo.

Theorem. Inani esuselwe ilingana nenani lezinombolo of the ngemikhiqizo etholakale izingxenye: (a c +) = a '+ c'.

Ngokufanayo, lo mthetho kuyoba okusebenzayo esuselwe umehluko.
Umphumela danogo imithetho yokuzihlukanisa kwamangqamuzana ngokwemisebenzi yawo kuyinto Ebhala ngokugomela kokuthi esuselwe amagama ambalwa ilingana nenani lezinombolo imikhiqizo etholwe migomo.

Ngokwesibonelo, uma ufuna ukuthola esuselwe isisho (a + c-k) ', bese umphumela kuba ukubonakaliswa' + c 'k'.

Theorem. Umkhiqizo esuselwe imisebenzi zezibalo differentiable weyesi ilingana nenani lezinombolo ehlanganisa umkhiqizo iyisici sokuqala kuya esuselwe yesibili futhi umkhiqizo Isici sesibili kuya esuselwe kuqala.

Theorem is izibalo ebhaliwe kanje: (a * c) '= a * a' + a '* s. Umphumela theorem yisiphelo sesimiso ezingase isici njalo kule esuselwe umkhiqizo asikhiphele ngaphandle umsebenzi esuselwe.

Ngesimo isisho algebraic, lo mthetho kulotshiwe kanje: (a * c) = a * a ', lapho = const.

Ngokwesibonelo, uma ufuna ukuthola esuselwe isisho (2a3) ', umphumela uba impendulo: 2 * (A3) = 2 * 3 * 6 * A2 = A2.

Theorem. ubudlelwane esuselwe imisebenzi elilingana lihlela isilinganiso phakathi kwama umehluko we esuselwe numerator siphindwe zifana futhi izikhathi numerator le esuselwe zifana futhi esigcawini zifana.

Theorem is izibalo ebhaliwe kanje: (a / c) '= ( a' * a * i-c) / ^2.

Ekuphetheni, kubalulekile ukuba sicabangele isimiso umehluko imisebenzi oluyinhlanganisela.

Theorem. Kunikezwe fuktsii y = f (x), lapho sithi x = c (t), khona-ke y umsebenzi, maqondana t variable, ngokuthi eyinkimbinkimbi.

Ngakho, ngo-izingabunjalo we esuselwe umsebenzi esiyinhlanganisela siphathwa njengesivakashi esuselwe umsebenzi siphindwe esuselwe sub-imisebenzi yayo. Ukuze kube lula imithetho yokuzihlukanisa kwamangqamuzana ngokwemisebenzi yawo imisebenzi eziyinkimbinkimbi kukhona ngesimo itafula.

With ukusetshenziswa njalo kwaleli thebula kulula ukukhumbula amagama ahlobene. Ezinye izindaba zika-derivatives imisebenzi eziyinkimbinkimbi ingatholakala uma sisebenzisa imithetho yokuzihlukanisa kwamangqamuzana ngokwemisebenzi yawo imisebenzi eziye ezibekwe theorems futhi corollaries kubo.