Ainihin dokoki na bambantawa, shafi lissafi

Don fara, yana da daraja ambaton cewa irin wannan bambanci da kuma ilmin lissafi ma'anar shi daukawa.

Bambanci aiki ne samfurin na wanda aka samu aiki na da hujja a kan bambanci da shaida. Shifran, wannan ra'ayi za a iya rubuta a matsayin magana: DY = y '* DX.

Bi da bi, don sanin ko wanda aka samu daga cikin daidaici y '= Lim DX-0 (DY / DX), kuma domin sanin iyaka ba - da magana DY / DX = x' + α, inda siga α ne infinitesimal ilmin lissafi yawa.

Saboda haka, bangarorin biyu na magana ya kamata a yawaita da DX, abin da kyakkyawan ba DY = y '* DX + α * DX, inda DX - shi ne wani infinitesimal canji a cikin shaida, (α * DX) - darajar wanda za a iya yi sakaci, sa'an nan DY - increment ayyuka, kuma (y * DX) - babban ɓangare na increment ko bambanci.

Bambanci aiki ne samfurin na wanda aka samu aiki a kan bambanci da shaida.

Yanzu ya zama dole a yi la'akari da asali dokoki na bambantawa, wanda sukan yi amfani da ilmin lissafi analysis.

Theorem. Wanda aka samu adadin daidaita da Naira Miliyan Xari da kayayyakin samu daga gyara: (a + c) = wata '+ c'.

Hakazalika, wannan mulki zai zama mai aiki domin wanda aka samu daga cikin bambanci.
A sakamako danogo dokoki na bambantawa ne tabbatarwa cewa wanda aka samu da wani yawan sharuddan daidaita da Naira Miliyan Xari da kayayyakin samu ta hanyar wadannan sharuddan.

Alal misali, idan kana so ka sami wanda aka samu da magana (mai + c-k) ', sa'an nan kuma sakamakon haka ne nuna wani' + c 'k'.

Theorem. The wanda aka samu samfurin daga ilmin lissafi ayyuka differentiable a wata aya daidai da Naira Miliyan Xari kunshi samfurin na farko factor zuwa na biyu wanda aka samu da samfurin na biyu factor zuwa na farko wanda aka samu.

Theorem ne shifran rubuta kamar haka: (a * c) '= wani * a' + wani '* s. A saboda abin da na Theorem ne a ƙarshe cewa akai factor a cikin wanda aka samu daga cikin samfurin iya dauka waje da wanda aka samu aiki.

A cikin nau'i na wani algebraic magana, wannan mulki aka rubuta kamar haka: (a * c) = wata * a ', inda wani = const.

Alal misali, idan kana so ka sami wanda aka samu da magana (2a3) ', sakamakon shi ne amsar: 2 * (A3) = 2 * 3 * 6 * A2 = A2.

Theorem. Wanda aka samu dangantakar ayyuka, sunã daidaita da rabo tsakanin bambanci na wanda aka samu daga cikin numerator yawaita ta hada da numerator sau da wanda aka samu daga cikin hada da square na maimaita lamba.

Theorem ne shifran rubuta kamar haka: (a / c) '= ( a' * a * a-c ') / ^2.

A ƙarshe, shi wajibi ne a yi la'akari da mulki ga bambance kumshin ayyuka.

Theorem. Ba wani fuktsii y = f (x), inda x = c (t), sa'an nan da aiki y, tare da girmamawa ga m t, da ake kira da hadaddun.

Saboda haka, a cikin ilmin lissafi bincike na wanda aka samu da wani kumshin aiki da aka bi a matsayin wanda aka samu daga cikin aikin yawaita da wanda aka samu daga cikin sub-ayyuka. Domin saukaka dokoki na bambantawa hadaddun ayyuka ne a cikin nau'i na wani tebur.

Tare da na yau da kullum da yin amfani da wannan tebur suna da sauki tuna Kalam. Sauran Kalam na hadaddun ayyuka za a iya samu, idan muka yi amfani da dokoki na bambantawa na ayyuka da cewa an saita kawo a cikin theorems da corollaries zuwa gare su.