Ka walaʻauʻana rula o ka differentiation, noi makemakika

E hoʻomaka, ia mea kumukuai hoomanao ana ia palena pau, a me ka makemakika manaʻo ka mea, hāpai.

Palena pau papa o ka huina hoonui o ka derivative hana o ka manaʻo hoʻopiʻi kū'ē ma ka palena pau o ka loulou. Mathematically, ua manaʻo hiki ke palapalaia e like me ka 'aoʻao o: dy = y me' * dx.

I huli ai oe, e hooholo i ka derivative o ka like y me '= Lim dx-0 (dy / dx), a e hooholo i ke kali - ka hōʻike dy / dx = m' + α, ma ka aiao α mea infinitesimal makemakika a pau.

Nolaila, e e hoonuiia na aoao a elua o ka olelo ma ka dx, a ultimately haawi dy = y me '* dx + α * dx, kahi dx - mea he infinitesimal loli i loko o ka manaʻo hoʻopiʻi kū'ē, (α * dx) - i ka waiwai o ka i hiki ke malama ole, a laila, dy - xi oihana, a (y me * dx) - ke kumu nui loa o ke xi a me ka palena pau.

Palena pau papa o ka huina hoonui o ka derivative hana ma ka palena pau o ka loulou.

Ano ka mea, Ua pono, e noonoo i ka walaʻauʻana rula o ka differentiation, i mea pinepine ia ma ka makemakika Ka Ikepili.

Theorem. Derivative dala a like me ka huina o nā huahana loaa mai eiiiiiaiou: (he + c) = ka '+ pela aku'.

Like me, keia rula e e hana no ka derivative o ke koena unuhi.
Ke no danogo rula o ka differentiation o ka assertion i ka derivative o ka helu o nā hua'ōlelo like me ka huina o nā huahana loaa mai ma kēia mau hua'ōlelo.

No kekahi laʻana, ina e makemake, e huli i ka derivative o ka hōʻike (i + e-k) ', laila, i ka hopena o ka olelo ana o kekahi' + pela aku 'K'.

Theorem. Ke derivative huahana o ka makemakika oihana differentiable ma kekahi wahi e like no ka huina oia hoi o ka huina hoonui o ka ololi mua a hiki i ka lua o ka derivative a me ka huina hoonui o ka lua o ka ololi a hiki i ka derivative mua.

ua mathematically palapala Theorem like penei: (he * c) '= ke * he' + he '* mau. Ke no o ka theorem mea he hopena i ka a eia i nā kumumea i loko o ka derivative o ka huina hoonui i e ia mawaho o ka derivative kuleana pili i.

Ma ke ano o ka algebraicʻana, ua kākau i kēia rula like penei: (he * c) = ka * i ', kahi i = const.

No kekahi laʻana, ina e makemake, e huli i ka derivative o ka hōʻike (2a3) ', i ka hopena o ka pane: 2 * (A3) = 2 * 3 * 6 * A2 = A2.

Theorem. Derivative pili oihana like i ka lākiō ma waena o ke koena unuhi o ka derivative o ka numerator hoonuiia e ka denominator, a me ka numerator manawa ka derivative o ka denominator, a me ka hale o ka denominator.

ua mathematically palapala Theorem like penei: (he / c) '= ( he' * i * ka-e ') / ^2.

Ma ka hopena, ka mea i pono, e noonoo i ka rula no ka differentiating lua hana.

Theorem. Ua haawiia he fuktsii y me = f (x), kahi m = c. (K), a laila, i ka papa y me, me ka pili ana i na ee iaaanu aey t, kapa aku la i ka luna '.

Ke'ī mai, ma ka makemakika Ka Ikepili o ka derivative o ka lua papa ua malamaia lakou nei, me he derivative o ka papa hoonuiia e ka derivative o kona iiaciiie-hana. No ka pono o na rula o ka differentiation o ka luna 'oihana i loko o ka palapala o ka papaʻaina.

Me ka pololei, hoʻohana i kēia papa e oluolu e hoomanao nā mea loaʻa. Ke koena o na nā mea loaʻa o ka luna 'oihana Hiki ke loaʻa, ina ua pili i ka rula o ka differentiation o ka oihana i i ua hookuu aku la i loko o ka theorems a corollaries ia ia.