Mau kumu makemakika Ka Ikepili. Pehea e huli i ka derivative?

Derivative o ka papa f (x) ma kekahi mau 'wahi x0 kuleana pili i kapa ulu hiʻohiʻona ka palena a hiki i ka xi o ka manaʻo hoʻopiʻi kū'ē, nae ia m i e 0, a me ka mokuna i koe. Derivative nui i koho hahauʻana, i kekahi manawa, Via wahi paha i kekahi palena pau. Pinepine, i ka derivative o ke kea-palena aʻe hualoaʻa, no ka mea, o ka hoohalike ai ua kākaʻikahi i hoʻohana.

Launch, a i ka derivative ma kekahi welau x0, kapa differentiable ma ia he wahi. Lawe, D1 - he iiiaanoaa o nā kumu ma i ka papa. F ua differentiated. Ka lanakila i kela a me keia i kekahi o na huahelu m, no D. F '(m), ua loaa i ka papa inoa āpana D1. Kēia hana i derivative o y me = f (x). Ua hoʻokohu 'ia:. F' (m).

Eia kekahi, o ka derivative mau hoʻohana 'ia ma ke kālaikūlohea a me ka hana' enekinia,. he mea kumu noonoo. I ka meaʻoi ma luna o neʻe aku i kekahi i kahi kūlike o (axis), ka wā noi i ke kānāwai o ke noi, i ua, X-i kahi kūlike o kēia wahi, ua ikeia ka m ( 'ole) kuleana pili i. Iloko o ka manawa wā mawaena mai t0 e t0 + 'ole lākou, i ka pohupani hale o ka wahi m (t0 + Halau) -x (t0) = m, a me kona māmā holoʻawelike V (Halau) like i ka m /' ole.

I kekahi manawa, i ke ano o ke noi imua o laila i ka māmā holoʻawelike 'aʻole e hoʻololi i ka poe liilii, manawaʻanuʻu, la me ka manao e holo me ka degere nui o ka pololei ua manaoia e eʻaʻahu. ʻOkoʻa, i ka nui o ka awelika mämä holo ina t0 keia i kekahi mau loa kūlike loa waiwai, a ua haawi ia ia e like me ka instantaneous māmā V (t0) i wahi ma kekahi mau manawa o ka manawa t0. Ua Ua manaoio aku i ka instantaneous māmā V (Halau) ua ike no kekahi papa m differentiated (k), i ka V (Halau) mea like i ka m '(' ole). Aloha kau, i ka mämä holo - ia mea he derivative o ka wahi o ka manawa.

Instantaneous māmā holo i nā maikaʻi a me ka io cia, a me ka waiwai o 0. Inā ia mea i kekahi manawa wā mawaena (t1, t2) He 'oluʻolu, alaila, i ka wahi e neʻe aku i loko o ka e like me mamua, a laila, m (k) i kahi kūlike o, piʻi pū me ka manawa, a ina V (, t) mea io, alaila, i ka i kahi kūlike o m ( 'ole) emi.

I hou eiiieaena hoopii, i ka wahi kolo ana ma ka pelane, a ma ka lewa. A laila, i ka māmā holo o - he maʻi lele a pau, a me nā hoʻoholo kēlā o ka wahi o ka maʻi lele V ( 'ole).

Like me, kekahi ke hoohalike i ka hoʻonui o ka wahi. Speed mea he hana o ka manawa, 'o ia hoʻi, V = V (' ole). A derivative o ia i kekahi kuleana pili i - ka noi hoʻonui: i = V '(' ole). Oia hoi, e huli mai ia i ka manawa derivative o ka mämä holo ka hoʻonui.

Ina y me = f (x) - kekahi differentiated kuleana pili i. A laila mākou e hiki ke noonoo i ke noi ana o ka wahi ma luna o ka i kahi kūlike o (axis), i lawe wahi no ke kānāwai He m = f ( 'ole). Mechanical malama o ka derivative, oia ka manawa e hoʻolako i akaka ano o na theorems o ka palena pau calculus.

Pehea e huli i ka derivative? Loaa i ka derivative o kekahi kuleana pili i ua kapaia kona differentiation.

E kau kou mau examples o ana e imi i ka derivative o ke kuleana pili i:

Ke derivative o kekahi mau papa e like me 'Aʻohe; derivative o ka papa y me = m mea like me ke kuʻikahi,.

A pehea i loaʻa i ka derivative o ka mahele? E hana i kēia, noonoo i ka i kēia mea:

No kekahi x0 <> 0 mākou i

y me / m = -1 / x0 * (m + m)

Aia nō kekahi rula, pehea e imi i ka derivative. oia:

Inā ka mana A a me B i differentiated wahi x0, laila lākou huina ua differentiated i ka wahi: (A + B) '= A' + B '. Aloha kau, i ka derivative o ke dala e like me ka huina o na nā mea loaʻa. Inā ke kuleana pili i ua differentiated ma kekahi wahi, a laila ka mea pono xi i ka 'Aʻohe ka wā ma hope o ka manaʻo hoʻopiʻi kū'ē i ka' Aʻohe o koʻu pomaikai ia.

Inā ka mana A a me B i differentiated wahi x0, laila, ua differentiated lākou huahana ma: (A * B) '= A'B + AB'. (Values oihana a me kā lākou nā mea loaʻa i ho omaulia ma ka welau x0). Inā ka papa A (m) ua differentiated ma ka wahi x0, a me C - ikaika, alaila, ua differentiated CA hana ma keia wahi, a (CA) '= CA'. Ia mea, he ikaika ololi ia ma waho o ka hoailona o ka derivative.

Inā ka mana A a me B i differentiated wahi x0, a me ka papa B mea,ʻaʻole like ia 'Aʻohe, laila kekahi differentiated lākou lākiō ma: (A / B)' = (A'B-AB ') / B * B.