Ka kōpo mphe tlhaloso e khutšoanyane ea se boleloang ke derivative.
Context:Ka thuto ea lipalo, derivative ea mosebetsi oa sebele polygonal mehato ea nahanela ho fetola ea mosebetsi boleng (khumo boleng) mabapi le phetoho e ka ngangisano ea eona (input boleng). Li-derivative ke sesebelisoa sa motheo sa calculus. Ka mohlala, motsoako oa boemo ba ntho e tsamaeang mabapi le nako ke lebelo la ntho: sena se lekanya hore na boemo ba ntho bo fetoha kapele hakae ha nako e ntse e tsamaea.  The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. Moeli o otlolohileng ke moeli o otlolohileng oa mosebetsi o haufi le boleng boo bo kenngoeng. Ka lebaka lena, derivative e atisa ho hlalosoa e le "sekhahla sa phetoho ea hang-hang", karolelano ea phetoho ea hang-hang ea ho feto-fetoha ho itšetlehileng ka ho feto-fetoha ho ikemetseng.  Li-derivative li ka sebelisoa ka kakaretso ho mesebetsi ea mefuta e mengata ea sebele. Ka generalization ena, derivative e hlalosoa e le phetoho ea linear eo graph ea eona e leng (kamora phetolelo e loketseng) e leng approximation e ntle ka ho fetisisa ea linear ho graph ea ts'ebetso ea pele. Matrix ea Jacobian ke matrix e emelang phetoho ena ea linear mabapi le motheo o fanoeng ke khetho ea mefuta e ikemetseng le e itšetlehileng ka eona. E ka baloa e le e tsoang ho e 'ngoe ea lintho tse sa tsejoeng tse sa tsejoeng. Bakeng sa mosebetsi oa bohlokoa ba sebele oa mefuta e'maloa, matrix ea Jacobian e fokotsa ho vector ea gradient.  Mokhoa oa ho fumana motsoako o bitsoang phapang. Ts'ebetso e fapaneng le ena e bitsoa ho se khetholle. Theorem ea motheo ea calculus e ama antidifferentiation le integration. Ho khetholla le ho kopanya ke mesebetsi e'meli ea motheo ea calculus e nang le phapang e le 'ngoe.
Ho tsoa ho eona ke mosebetsi o lekanyang kutloelo-bohloko ea ho fetola mosebetsi o hlahisoang o thehiloe liphetohong tse kenang. Ka mohlala, hore na boemo ba ntho bo tsamaea ka potlako hakae nakong e itseng (ke hore, motsoako oa boemo mabapi le nako) ke lebelo la ntho eo.