Ngicela ungichazele kafushane ukuthi kusho ukuthini okuvelayo.
Context:Ezemathematics, i-derivative yomsebenzi we-real variable ilinganisa ukuzwela ekuguqulweni kwenani lomsebenzi (inani lokukhipha) maqondana nokushintsha kwe-argument yayo (inani lokufaka). Iziqalo ziyithuluzi eliyisisekelo le-calculus. Ngokwesibonelo, isilinganiso sesimo sento ehambayo ngokuqondene nesikhathi sibizwa ngokuthi isivinini sento: lokhu kulinganisa ukuthi isikhundla sento sishintsha ngokushesha kangakanani njengoba isikhathi sihamba.  I derivative of a umsebenzi of a variable olulodwa at a value okukhethiwe input, lapho likhona, kuyinto emthambekeni we line tangent kuya igrafu umsebenzi ngaleso sikhathi. I-tangent line iyona engcono kakhulu eseduze nomsebenzi oseduze nalelo nani. Ngenxa yalesi sizathu, i-derivative ivame ukuchazwa ngokuthi "izinga lokuguquka okusheshayo", isilinganiso sokuguquka okusheshayo kokuguquguqukayo okuxhomeke kulokho okuguquguqukayo okuzimele.  Iziqalo zingasetshenziswa kabanzi emisebenzini yezinguquko eziningana zangempela. Kulokhu kuhlanganisa, okuvelayo kuhunyushwa kabusha njengokuguqulwa okuqondile okuyi-graph yayo (ngemuva kokuhumusha okufanelekile) ukusondela okuhle kakhulu okuqondile ku-graph yomsebenzi wokuqala. I matrix Jacobian kuyinto matrix ukuthi limelela lokhu ukuguqulwa eqondile maqondana isisekelo esinikezwe ukukhethwa okuhlukile ezimele futhi kuncike. Ingalinganiswa ngokuya ngemikhiqizo engatheni maqondana nezinguquko ezizimele. Ukuze uthole umsebenzi onenani langempela lezinto eziguquguqukayo eziningana, i-jacobian matrix iyancipha ibe yi-gradient vector.  Inqubo yokuthola okukhishwayo ibizwa ngokuthi ukuhlukanisa. Inqubo ephambene nayo ibizwa ngokuthi i-antidifferentiation. I-fundamental theorem ye-calculus ihlobanisa ukuhlukaniswa okuphambene nokuhlanganiswa. Ukwehlukanisa nokuhlanganisa kuyizinto ezimbili eziyisisekelo ezenziwa kuyi-calculus enezinto eziguquguqukayo.
I-derivative iwumsebenzi olinganisa ukuzwela ukushintsha okukhiphayo komsebenzi ngokusekelwe ekushintsheni kokungenayo. Isibonelo, ukuthi isikhundla sento sihamba ngokushesha kangakanani esikhathini esichaziwe (okungukuthi, isenzo sesikhundla maqondana nesikhathi) yisivinini sento.