Saldhigyadii falanqaynta xisaabta. Sida loo helo derivative ah?

Derivative of f a function (x) xaflad x0 dhibic gaar ah u yeedhay ratio koritaanka xad u go'an inremantiga ee doodda, in x in ay 0, iyo soohdinta ka jira. Derivative guud ahaan loogu talagalay stroke, mararka qaarkood via dhibic ama via kala duwan ah. Inta badan, derivative of gudba xuduudaha natiijada marin habaabin ah, tan iyo matalaad noocan oo kale ah waxaa dhif ah loo isticmaalo.

Function, taas oo uu leeyahay derivative ee x0 a dhibic gaar ah, loo yaqaan differentiable barta noocan oo kale ah. U qaadan, D1 - hannaanka ka mid ah dhibcood ee f function waxaa lagu kala. Howl si kasta oo mid ka mid ah lambarada x, ka tirsan D f '(x), waxaan aad u hesho meesha magaca function D1. function Tani waa derivative of y = f (x). Waxaa loogu talagalay sida: f '(x).

Intaas waxaa sii dheer, derivative ee caadi ahaan loo isticmaalo in physics iyo injineernimada. Ka fiirso tusaale fudud. The wax dhibic guuro on dhidibka a duwo, markii la weydiiyay waxa uu sharcigu ka mid ah mooshinka, oo la, x-duwo of markan waxaa loo yaqaan x (t) shaqo. Inta lagu guda jiro bareeg waqti ka t0 in t0 + t Shurako barakaca ee x dhibic (t0 + t) -x (t0) = x, iyo celcelis ahaan v xawaaraha (t) in loo siman yahay x / t.

Mararka qaarkood nooca mooshinka soo bandhigay si xawaaraha celcelis ahaan aysan waxba ka beddelin dura waqti yar, taasoo la micno ah in dhaqdhaqaaqa la degree weyn oo sax ah waxaa loo arkaa inay uniform. Haddii kale, ee qiimaha celceliska xawaaraha haddii t0 soo socota in ay qaar ka mid ah qiimaha gabi ahaanba sax ah, oo waa in loo gudbiyaa sida v xawaaraha degdeg ah (t0) dhibic in la joogo gaar ah oo t0 waqti. Waxaa la rumeysan yahay in v xawaaraha degdeg ah (t) lagu yaqaan wax x kala function (t), waxa v (t) waa loo siman yahay si x '(t). Si fudud u gelin, xawaaraha - waa derivative ka mid ah isku waqti.

xawaare degdeg ah ayaa qiimaha wanaagsan iyo wax xunba, iyo qiimaha waa 0. Haddii ay tahay at bareeg ah oo waqti (T1, T2) waa ay wanaagsan tahay, ka dibna u dhaqaaqdo dhibic isku jiho ah, i.e., x (t) duwo korodhka waqti, iyo haddii v (t) waa negative, ka dibna ku duwo x (t) hoos.

Xaaladaha qalafsan dheeraad ah, barta dhaqdhaqaaqa diyaarada ama in meel bannaan oo. Markaas xawaare ka mid ah - tiro dulinka ah, iyo go'aan ka kasta oo ka mid ah wadataa of v dulinka ah (t).

Sidoo kale, mid ka mid is barbardhigi kartaa xawaaraha ee barta. Speed waa shaqo waqti, ie, v = v (t). derivative A shaqada noocan oo kale ah - dardargelinta mooshinka: a = v '(t). In uu yahay, waxaa soo baxday in derivative wakhtiga xawaaruhu yahay dardargelinta.

Ka soo qaad y = f (x) - shaqo kasta oo kala duwan. Haddaba, waxaan ka fiirsan kartaa mooshinka of dhibic on dhidibka duwo, kaas oo ka dhici waayo, sharcigu x = f ah (t). dayactirka farsamo ee derivative ku siinayaa fursad si ay u bixiyaan fasiraad cad oo ku aragti ah ee kalkulaska kala duwan ee.

Sida loo helo derivative ah? Helitaanka derivative ah ee shaqada ah waxa loo yaqaan ay ku kaladuwan yihiin.

Dhig tusaale u ah sida loo helo derivative ee shaqada aad:

derivative ee shaqo joogto ah loo siman yahay si eber, derivative of y = x shaqada waa loo siman yahay si ay midnimo.

Iyo sida loo helo derivative ee jajabka? Si arrintan loo sameeyo, ka fiirsan waxyaabaha soo socda:

Waayo, x0 kasta oo <> 0 waxaan leenahay

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

Waxaa jira sharciyo qaar ka mid ah, sida in la helo derivative ah. kuwaas oo:

Haddii hawlaha A iyo B waa x0 dhibic kala duwan, ka dibna ay soo tiriya waxaa loo kala at hal dhibic: (A + B) = A '+ B'. Si fudud u gelin, derivative of lacag si siman u soo tiriya reer reer taagayo ah. Haddii shaqo la kala barta qaar ka mid ah, markaas waa in inremantiga eber marka kadib muran in ay eber faa'iido.

Haddii hawlaha A iyo B waa x0 dhibic kala duwan, ka dibna ay wax soo saarka waxaa kala ah: (* B A) '= A'B + AB'. (Qiimayaasha hawlaha iyo taagayo waxaa loo xisaabiyaa at x0 dhibic). Haddii shaqo A ee (x) waa kala ee x0 dhibic, iyo C - joogto ah, ka dibna shaqo CA waa kala markan iyo (CA) '= CA'. Taasi waa, arrin joogto ah loo qaaday meel ka baxsan calaamada derivative ah.

Haddii hawlaha A iyo B waa x0 dhibic kala duwan, iyo shaqada B ma qummana in eber, ka dibna ay ratio sidoo kale kala ah: (A / B) = (A'B-AB) / B * B.