Kev Kawm Lej Hauv Tsev Kawm Ntawv Theem Siab

Cov Kev Siv ntawm Derivatives hauv Ntau Qhov Kev Tshawb Fawb Txog Kev Tshawb Fawb Qhov derivative yog lub tswv yim tseem ceeb hauv calculus, uas tau qhia los ntawm Sir Isaac Newton thiab Gottfried Wilhelm Leibniz thaum xyoo pua 17th. Hauv kev suav lej, qhov derivative sawv cev rau qhov kev hloov pauv ntawm ib qho kev ua haujlwm nrog rau ib qho ntawm nws cov hloov pauv. Lub tswv yim no tsis yog tsuas yog qhov tseem ceeb rau kev suav lej nws tus kheej xwb tab sis kuj muaj kev siv dav hauv… Nyeem ntxiv

Cov Qhab Nia Kawg ntawm Qhov Tsawg Kawg Nkaus thiab Qhov Siab Tshaj Plaws Rov Qab Los ​​Hauv kev suav lej thiab kev tshuaj xyuas, lub tswv yim ntawm cov qhab nia kawg yog qhov tseem ceeb, ob qho tib si hauv ntau qhov kev tshawb fawb thiab hauv kev siv txhua hnub. Cov qhab nia kawg, uas xa mus rau cov qhab nia ntawm daim duab ntawm ib qho kev ua haujlwm uas qhov kev ua haujlwm mus txog nws qhov tsawg kawg nkaus lossis qhov siab tshaj plaws, ua lub luag haujlwm tseem ceeb hauv kev txheeb xyuas cov yam ntxwv tseem ceeb ntawm… Nyeem ntxiv

Kev Ua Haujlwm Ntau Ntxiv, Kev Txo Cov Haujlwm, thiab Cov Haujlwm Nyob Ruaj Khoov: Kev Tshawb Fawb thiab Kev Siv Hauv kev suav lej, tshwj xeeb tshaj yog hauv kev suav lej thiab kev tshawb fawb, lub tswv yim ntawm kev ua haujlwm yog lub hauv paus tseem ceeb uas tso cai rau peb piav qhia thiab nkag siab txog ntau yam ntawm cov xwm txheej ntuj thiab dynamic. Ib qho ncauj lus nthuav los tham txog yog kev nce cov haujlwm, kev txo cov haujlwm, thiab cov haujlwm nyob ruaj khov. Cov no yog… Nyeem ntxiv

Kab Sib Npaug Tangent rau Ib Qho Nkaus Hauv kev suav lej, kab sib npaug ntawm kab sib npaug rau ib qho nkhaus ua lub luag haujlwm tseem ceeb hauv kev nkag siab txog ntau yam xwm txheej, ob qho tib si hauv kev tshawb fawb thiab kev tsim kho, thiab hauv kev siv txhua hnub. Kab sib npaug rau ib qho nkhaus yog ib txoj kab uas kov qhov nkhaus ntawm ib qho chaw tshwj xeeb xwb. Txhawm rau kom nkag siab ntxiv txog lub tswv yim no, peb yuav tsum nkag siab nws cov lus txhais, kev siv, thiab… Nyeem ntxiv

Cov Kev Siv ntawm Derivatives hauv Kev Tshawb Fawb thiab Kev Siv Tshuab Derivatives yog lub tswv yim tseem ceeb hauv kev suav lej uas siv dav hauv ntau qhov chaw ntawm kev tshawb fawb thiab thev naus laus zis. Lub tswv yim ntawm derivative ntsuas seb qhov kev ua haujlwm hloov pauv li cas thaum nws cov tswv yim hloov pauv. Tsab xov xwm no yuav tham txog ntau yam kev siv ntawm derivatives hauv ntau qhov chaw tseem ceeb, suav nrog physics, economics, biology, engineering, thiab computer science, ... Nyeem ntxiv

Txoj Cai Chain hauv Derivatives Kev suav lej ua lub luag haujlwm tseem ceeb hauv ntau yam ntawm lub neej, los ntawm kev tshawb fawb mus rau kev lag luam. Ib qho tseem ceeb hauv calculus yog lub tswv yim ntawm derivative. Derivatives muab txoj hauv kev los nkag siab txog kev ua haujlwm hloov pauv li cas thaum cov hloov pauv hloov pauv. Ib qho ntawm cov tswv yim tseem ceeb tshaj plaws hauv differential calculus yog txoj cai saw... Nyeem ntxiv

Cov Kev Cai Lij Choj ntawm Trigonometric Functions Hauv kev kawm lej siab heev, tshwj xeeb yog calculus, peb feem ntau ntsib cov kev cai lij choj trigonometric xws li sine (sin), cosine (cos), secant (sec), cosecant (csc), tangent (tan), thiab cotangent (cot). Hauv qhov no, kev nkag siab txog cov kev cai lij choj ntawm cov kev cai lij choj no yog qhov tseem ceeb, tshwj xeeb tshaj yog rau cov ntawv thov hauv physics, engineering, thiab computer science. Tsab xov xwm no yuav tshuaj xyuas lawv kom meej… Nyeem ntxiv

Algebraic Derivatives of Functions: Ib Phau Ntawv Qhia Tag Nrho Cov derivative ntawm ib qho kev ua haujlwm yog lub tswv yim tseem ceeb hauv calculus thiab lej feem ntau. Lub tswv yim no tsis yog siv rau hauv kev xav xwb tab sis kuj muaj kev siv tau hauv ntau qhov chaw, suav nrog physics, engineering, economics, thiab computer science. Tsab xov xwm no yuav tham txog algebraic derivative ntawm cov haujlwm, los ntawm nws cov lus txhais yooj yim mus rau nws cov ntawv thov… Nyeem ntxiv

Cov Khoom ntawm Derivative ntawm Ib Lub Function Qhov derivative ntawm ib lub function yog lub tswv yim tseem ceeb hauv calculus uas ntsuas qhov kev hloov pauv ntawm ib lub function ntawm ib qho chaw. Derivatives muab cov kev nkag siab tseem ceeb rau hauv tus cwj pwm thiab cov khoom ntawm cov functions, suav nrog qhov kev nyiam ntawm lawv cov nqi kom nce lossis txo qis, tig cov ntsiab lus, thiab lwm yam ntaub ntawv tseem ceeb. Hauv tsab xov xwm no, peb yuav tham txog ntau yam khoom ntawm derivative ntawm ib lub function thiab lawv cov ntawv thov hauv… Nyeem ntxiv

Kev Sau Cov Lus Qhia Txog Kev Ua Haujlwm (Derivative) Kev Taw Qhia Hauv kev lej, tshwj xeeb yog calculus, cov lus qhia txog kev ua haujlwm yog lub tswv yim tseem ceeb uas ua lub luag haujlwm tseem ceeb hauv ntau yam kev siv. Cov lus qhia txog kev ua haujlwm tsis yog siv hauv kev lej theoretical xwb tab sis kuj siv hauv kev tshawb fawb, engineering, economics, thiab ntau lwm yam kev qhuab qhia. Tsab xov xwm no yuav tham txog kev sau cov lus qhia txog kev ua haujlwm kom ntxaws, suav nrog nws cov hauv paus, cov cai tseem ceeb, thiab cov piv txwv ntawm kev siv. … Nyeem ntxiv