Zvigadziko kwemasvomhu ongororo. How kuwana rinobva?

Rinobva ane basa add (x) pane imwe nguva x0 basa rinonzi kukura reshiyo muganhu kuti increment renharo, akapa kuti X kuva 0, uye muganhu ariko. Kazhinji rinobva yakasarudzwa sitiroko, dzimwe nguva vachishandisa pfungwa kana vachishandisa mumwe differential. Kazhinji, rinobva muchinjikwa-muganhu anotsausa zvabuda, sezvo yakadaro mufananidzo haawanzopiwi kushandiswa.

Basa, chine rinobva pane imwe nguva x0, akadana differentiable panguva yakadaro pfungwa. Kufunga, D1 - a muzvizhinji pfungwa panguva iyo basa f kusiyaniswa. Rakavapa mumwe nomumwe nhamba X, ndeve D add '(x), isu kuwana basa rokuti nzvimbo D1. basa Iri rinobva pane ja = d (x). Akasarudzwa sezvo: f '(x).

Uyezve, rinobva yaiwanzoshandiswa wefizikisi uye ouinjiniya. Funga muenzaniso nyore. The zvinhu Pfungwa inofamba iri batanidza akabatana, kana akabvunza chii mutemo inofamba, ndiko, x-batanidza pfungwa iyi inozivikanwa X (T) ushande. Panguva penguva kubva t0 kusvikira t0 + T vakaenzana kuti misha iri pfungwa X (t0 + T) -x (t0) = X, uye ayo avhareji nokukurumidza V (t) akaenzana X / t.

Dzimwe mhando rakaramba akapa kuitira kuti avhareji nokukurumidza haachinji panguva diki nguva zvikamu, zvichireva kuti kufamba pamwe mukuru dhigirii zvakarurama anoonekwa kuti rekuchikoro. Neimwe nzira, ari kukosha avhareji nokukurumidza kana t0 anotevera kune vamwe zvachose chaiwo kukosha, uye anonzi ari nguva imwe nokukurumidza V (t0) kuti pana imwe nguva nguva t0. Zvinonzi vaidavira kuti nguva imwe nokukurumidza V (t) anozivikanwa chero kusiyaniswa nerevane X (T), panguva ipi vs. (T) akaenzana x '(T). Zvichitaurwa zviri nyore, nokukurumidza - payo rinobva pakati Coordonatele nguva.

Nguva imwe velocity ane zvose zvakanaka nezvakaipa tsika, uye mutengo uri 0. Kana pane imwe nguva penguva (T1; t2) iri zvakanaka, zvino pfungwa zvinopfakanyika chete mirayiridzo, i.e., X (T) batanidza kuwedzera pamwe nguva, uye kana V (t) ndiko kunaka, ipapo rinoronga X (t) kunoderedza.

In zvakawanda dzakaoma kunzwisisa, pfungwa zvinopfakanyika mundege kana muchadenga. Ipapo velocity pakati - a Vector uwandu, uye anosarudza nomumwe Coordonatele ane Vector V (t).

Saizvozvowo, munhu anogona kusiyana kumhanyisa yacho pfungwa. Speed iri kushanda nguva, kureva, v = vs. (T). A rinobva ane basa kwakadaro - inofamba kumhanyisa: a = vs. '(T). Kureva zvinoitika kuti nguva rinobva kuti nokukurumidza ndiyo kumhanyisa.

Ngatitii Y = d (x) - chero kusiyaniswa ushande. Zvadaro tinogona kufunga inofamba ane pfungwa pamusoro rinoronga akabatana, zvinotora nzvimbo mutemo x = d (T). Zvokuimba munyu wenyika rinobva anopa mukana kupa dudziro zvakajeka theorems ari differential calculus.

How kuwana rinobva? Kuwana rinobva ane basa anonzi Kusiyanisa kwayo.

Isa mienzaniso vako sei kuwana rinobva pakati mashandiro:

The rinobva pane kugara basa akaenzana razero; rinobva pane mashandiro and = X akaenzana kubatana.

Uye sei kuwana rinobva pamusoro hacho? Kuti aite izvi, funga mashoko anotevera:

Nokuti chero x0 <> 0 tine

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

Kune dzimwe mitemo, sei kuwana rinobva. zvinoti:

Kana mabasa A uye B zviri kusiyaniswa pfungwa x0, ipapo mari yavo kusiyaniswa pane imwe nguva: (A + B) '= A' + B '. Zvichitaurwa zviri nyore, kuti rinobva ane chitsama akaenzana makuru nomukaka. Kana basa iri kusiyaniswa pane imwe nguva, ipapo unofanira increment kuti razero apo vachitevera nharo kusvikira razero inopfumisa.

Kana mabasa A uye B zviri kusiyaniswa pfungwa x0, ipapo chigadzirwa kwavo kusiyaniswa at: (A * B) '= A'B + AB'. (Values mabasa avo nomukaka zviri dzaona achitandadza x0). Kana basa A (x) iri kusiyaniswa mu pfungwa x0, uye C - kugara, ipapo CA basa iri kusiyaniswa panguva ino uye (CA) '= CA'. Kureva, kugara chinhu wakatorwa kunze kwechiratidzo rinobva.

Kana mabasa A uye B zviri kusiyaniswa pfungwa x0, uye mashandiro B haana kuenzana zero, ipapo reshiyo kwavo kusiyaniswa pa: (A / B) '= (A'B-AB') / B * B.