Sezvo rinobva pamusoro cosine goho

The rinobva pakati cosine rakafanana rinobva kuna Sine hwaro uchapupu - tsanangudzo muganhu ishande. Zvinokwanisika kushandisa imwe nzira uchishandisa trigonometric zvokuimba kutinhisa Sine uye cosine pamakona. Taura chimwe basa pashure perimwe - kuburikidza sine wave cosine, Sine, uye kusiyana navo kunzwisisa nharo.

Funga nezvomuenzaniso goho kuti nzira yokutanga (Kosi (x)) '

Ipai kunyora nezvavo increment Δh nharo X kuti ja = Kosi (x). Kana kukosha mutsva nharo X + Δh kuwana kukosha itsva Kosi basa (x + Δh). Zvadaro increment Δu basa achava akaenzana Kosi (x + Δx) -Cos (x).
Nhamba yacho increment basa achava Δh yakadai: (Kosi (x + Δx) -Cos (x)) / Δh. Vhomora nokuzivikanwa transformations zvichiguma numerator pamusoro hacho. Recall yemaitiro musiyano cosines, zvinoguma basa -2Sin (Δh / 2) kane Sin (x + Δh / 2). Tinowana muganhu nevaNefirimu private chigadzirwa ichi Δh apo Δh uderedze razero. Zvinozivikanwa kuti wokutanga (ainzi kunoshamisa) muganhu nevaNefirimu (Sin (Δh / 2) / (Δh / 2)) akaenzana 1, uye kukutadzisa -Sin (x + Δh / 2) iri vakaenzana -Sin (x) apo Δx, achirapa razero.
Tinonyora mugumisiro: racho rinobva (Kosi (x)) 'ndiko - Sin (x).

Vamwe vanosarudza nzira vachiwana chete payakavakirwa wechipiri

Anozikamwa kuna trigonometry: Kosi (x) akaenzana Sin (0,5 · Π-x) Saizvozvowo Sin (x) ndiro Kosi (0,5 · Π-x). Zvadaro differentiable kunzwisisa basa - Sine ane zvimwe angled (pachinzvimbo X cosine).
Tawana chigadzirwa Kosi (0,5 · Π-x) · (0,5 · Π-x) ', nokuti rinobva pamusoro Sine cosine kuti X iri x. Kuwanikwa yechipiri inonyatsoita Sin (x) = Kosi (0,5 · Π-x) kutsiva cosine uye Sine, funga kuti (0,5 · Π-x) = -1. Zvino tinowana -Sin (x).
Saka, utore rinobva pakati cosine, isu '= -Sin (x) nokuti basa and = Kosi (x).

The rinobva pamusoro cosine akaenzana

A anowanzoshandiswa muenzaniso unoshandiswa apo rinobva pamusoro cosine. Mashandiro ja = Kosi ² (x) zvakaoma. Tinowana wokutanga differential simba mashandiro pamwe exponent 2, kureva 2 · Kosi (x), zvino zvikawanda nokuda rinobva (Kosi (x)) ', izvo zvakaenzana -Sin (x). Kuwana, y '= -2 · Kosi (x) · Chivi (x). Kana zvinoshanda Sin payakavakirwa (2 · x), Sine ari miviri yorusvingo, wana wokupedzisira Simplified
Kupindura Y '= -Sin (2 · x)

hyperbolic mabasa

Kureva kudzidza zvakawanda michina anoranga mu masvomhu Somuenzaniso, kuti zvive nyore kuti kuverenga integrals, mhinduro kubva differential equations. Ivo vakaratidza maererano trigonometric mashandiro pamwe zvekufungidzira nenharo, saka hyperbolic cosine AND ch (x) = Kosi (i · x) apo ini - chiri zvekufungidzira Unit, hyperbolic Sine hove dzakawanda (x) = Sin (i · x).
Hyperbolic cosine rinowanikwa nyore.
Funga basa and ^{= (e X + E -x)} / 2, ichi ndicho hyperbolic cosine AND ch (x). Achishandisa mutemo yokuwana rinobva Verengai mashoko maviri, kubviswa kazhinji kugara multiplier (Const) nokuti chiratidzo rinobva. The rokuti 0.5 rechipiri · e ^-x - kunzwisisa basa (yaro rinobva ndiko -0,5 · e ^-x), 0.5 · add ^X - wokutanga izwi. (CH (x)) '= ((e ^X + e ^{- x)} / 2)' anogona kunyorwa zvakasiyana: (0,5 · e · ^X + 0.5 e ^{- x)} '= 0,5 · e ^X -0,5 · e ^{- X,} nokuti rinobva (e ^{- x)} 'akaenzana -1, kuti umnnozhennaya e ^{- x.} Zvakaguma musiyano, uye ichi ndicho hyperbolic sine wave hove dzakawanda (x).
Mhedziso: (AND ch (x)) '= hove dzakawanda (x).
Rassmitrim muenzaniso sei kuverenga rinobva pakati mashandiro and = AND ch (x ³ +1).
By Kusiyanisa utongi hyperbolic cosine pamwe kunzwisisa nharo Y '= hove dzakawanda (x ³ +1) · (x ³ +1)' apo (x ³ + 1) = 3 · X ² + 0.
A: The rinobva pane basa ichi akaenzana 3 · X ² · hove dzakawanda (x ³ +1).

Dérivés akakurukura mabasa ja = AND ch (x) uye Y = Kosi (x) tafura

Panguva Mutongo mienzaniso haumanikidzwi nguva imwe neimwe kusiyanisa navo aronga zano, kushandisa goho zvakakwana.
Example. Kusiyanisa mashandiro and = Kosi (x) + Kosi ² (-x) -Ch (5 · x).
Zviri nyore kuti compute (kushandiswa tabulated Data), y '= -Sin (x) + Sin (2 · x) -5 · Sh (x · 5).