Litšebeliso tsa Li-Derivatives Mafapheng a sa Tšoaneng a Saense
Derivative ke mohopolo wa motheo ka hara dipalo, o hlahisitsweng ke Sir Isaac Newton le Gottfried Wilhelm Leibniz qetellong ya lekgolo la bo17 la dilemo. Dipalong, derivative e emela sekgahla sa phetoho ya mosebetsi mabapi le e nngwe ya diphetoho tsa wona. Kgopolo ena ha se ya motheo feela dipalong ka boyona empa hape e na le ditshebediso tse pharaletseng mafapheng a mang a fapaneng a saense. Sengoloa sena se tla tshohla ditshebediso tse fapaneng tsa derivatives mafapheng a fapaneng, ho tloha fisiks le moruo ho ya ho baeloji le boenjiniere ho ya ho saense ya dikhomphutha.
1. Fisiks
Di-derivative di bohlokwa haholo fisiks, haholoholo ho mechanics ya kgale. E nngwe ya mehlala ya motheo ke kamano pakeng tsa boemo, lebelo, le ho potlaka. Haeba \( s(t) \) e le boemo ba ntho e le mosebetsi wa nako, jwale:
– Lebelo (\( v(t) \)) ke letshwao la pele la boemo mabapi le nako: \( v(t) = \frac{ds(t)}{dt} \).
– Ho potlaka (\( a(t) \)) ke derivative ya pele ya lebelo kapa derivative ya bobedi ya boemo mabapi le nako: \( a(t) = \frac{dv(t)}{dt} = \frac{d^2s(t)}{dt^2} \).
Ho phaella moo, ho electromagnetism, molao oa Faraday oa induction ea electromagnetic o bolela hore matla a electromotive (EMF) a hlahisoang potolohong ke derivative ea flux ea makenete mabapi le nako.
2. Moruo
Moruong, di-derivatives di sebediswa ho sekaseka diphetoho ditshenyehelong, lekenong le mesebetsing ya tlhahiso. Mohlala:
– Litšenyehelo tsa Marginal (Biaya Marginal) ke derivative ea mosebetsi oa litšenyehelo tsohle mabapi le bongata ba tlhahiso, e leng se bontšang kamoo litšenyehelo tsohle li fetohang kateng ha tlhahiso e ntse e eketseha: \( MC = \frac{dTC}{dQ} \).
– Lekeno le ka Tlase (Lekeno le ka Tlase) ke derivative ya mosebetsi wa lekeno lohle mabapi le bongata ba tlhahiso, e hlalosang lekeno le eketsehileng ha thekiso e eketseha: \( MR = \frac{dTR}{dQ} \).
Tšebeliso e 'ngoe ea bohlokoa e khopolo-taba ea thuso. Mosebetsi oa thuso o hlalosa khotsofalo kapa thuso e fumanoang tšebelisong ea thepa le lits'ebeletso. Tšimoloho ea pele ea mosebetsi oa thuso e bitsoa thuso e nyane, e bontšang khotsofalo e eketsehileng e fumanoang ka ho sebelisa yuniti e eketsehileng ea thepa kapa tšebeletso.
3. Baeloji
Ho baeloji, di-derivatives di sebediswa ho etsa mohlala wa ditshebetso tse fapaneng tse fetohang. Mohlala, ho ecology, mehlala ya kgolo ya baahi hangata e sebedisa di-derivatives ho hlalosa sekgahla sa kgolo ya baahi. Mehlala ya kgolo ya exponential le logistic ke mehlala e mmedi e tlwaelehileng:
– Mohlala wa kgolo ya tlhahiso: \( \frac{dN}{dt} = rN \), moo \( N \) e leng boholo ba baahi mme \( r \) e le sekgahla sa kgolo ya tlhaho.
– Mohlala wa kgolo ya thepa: \( \frac{dN}{dt} = rN \left( 1 – \frac{N}{K} \right) \), moo \( K \) e leng bokgoni ba tikoloho mme \( \left( 1 – \frac{N}{K} \right) \) e le ntlha ya phokotso e fokotsang sekgahla sa kgolo ha bokgoni ba tikoloho bo atamelwa.
Ho fisioloji, di-derivatives di sebediswa ho etsa mohlala wa ditshebetso tsa fisioloji tse kang phallo ya madi le phetiso ya letshwao la methapo. Mohlala, molao wa Darcy wa phallo ya madi methapong ya madi o sebedisa di-derivatives ho hlalosa diphetoho kgatellong ya madi ka hara mothapo.
4. Mokhoa
Dintho tse tswang ho tsona di bohlokwa haholo makaleng a fapaneng a boenjiniere. Boenjiniereng ba meaho le ba mechini, dintho tse tswang ho tsona di sebediswa tlhahlobong ya sebopeho le metjhining ya mokelikeli. Mohlala:
– Tlhahlobong ea sebopeho, mokhoa oa karolo e lekanyelitsoeng o sebelisoa ho fumana libopeho le likhatello meahong. Setho sa ts'ebetso ea ho falla se fana ka khatello, 'me setho sa mofuta oa khatello se fana ka khatello.
– Mekhaniking ea mokelikeli, li-equation tsa Navier-Stokes li hlalosa phallo ea mokelikeli. Li-equation tsena ke li-equation tse fapaneng tse kenyelletsang li-derivative tse sa fellang tsa lebelo la mokelikeli mabapi le nako le sebaka.
Boenjiniere ba motlakase, di-derivative di sebediswa tlhahlobong ya dipotoloho tsa motlakase. Melao ya Kirchhoff le kgopolo ya marangrang hangata di kenyeletsa di-derivative ho hlalosa kamano pakeng tsa hajwale, motlakase, le inductance dipotolohong tsa motlakase.
5. Saense ea Khomphutha
Saenseng ea khomphutha, li-derivative li sebelisoa ho ntlafatsa le ho ithuta ka mochini. E 'ngoe ea lits'ebetso tse ka sehloohong ke ho ntlafatsa li-algorithms tse kang ho theoha ha gradient. Algorithm ena e sebelisetsoa ho fokotsa ts'ebetso ea litšenyehelo ts'ebetsong ea koetliso ea mohlala oa ho ithuta ka mochini:
– Gradient ke vekthara ya pele ya derivative ya mosebetsi wa ditjeo mabapi le diparamitha tsa mohlala, e leng se bontshang tsela ya phetoho e kgolo ka ho fetisisa.
– Ho theoha ha gradient ke ts'ebetso e pheta-phetoang e sebelisang li-gradient ho ntlafatsa liparamente tsa mohlala ho ea ho bonyane ba ts'ebetso ea litšenyehelo.
Ho phaella moo, ditshwantshong tsa khomphutha, di-derivative di sebediswa ho laola mabone le meriti. Molao wa Lambert le mohlala wa mabone wa Phong di sebedisa di-derivative ho bala matla a lesedi le bonahatswang ho tloha hodima bokahodimo bo pepeseditsweng mohloding wa lesedi.
6. Khemistri
K'hemistri, di-derivatives di sebediswa ho reaction kinetics ho hlalosa sekgahla sa karabelo ya dikhemikhale. Sekgahla sa karabelo hangata se hlahiswa e le derivative ya mahloriso a reactant kapa sehlahiswa mabapi le nako. Mohlala, bakeng sa karabelo ya pele:
\[ \text{Reactants} \rightarrow \text{Products} \]
Sekgahla sa karabelo \(r(t) \) se ka hlaloswa ka tsela ena:
\[ r(t) = – \frac{d[\text{Reactant}]}{dt} = \frac{d[\text{Product}]}{dt} \]
Ho phaella moo, di-derivative di sebediswa ho thermodynamics ho sekaseka diphetoho tsa matla tsamaisong. Mohlala, Gibbs free energy (G) ke mosebetsi wa thermodynamic o atisang ho sebediswa ho bolela esale pele tataiso ya dikarabelo tsa dikhemikhale, mme derivative ya pele ya G mabapi le maemo a tokoloho ya sistimi e fana ka tlhahisoleseding mabapi le boemo ba thermodynamic equilibrium.
Qetello
Ho tsoa tlhalosong e kaholimo, ho hlakile hore mohopolo oa li-derivatives o na le lits'ebetso tse pharaletseng mafapheng a fapaneng a mahlale. Fisiks, li-derivatives li hlalosa kamano ea motheo lipakeng tsa boemo, lebelo le ho potlaka. Moruong, li-derivatives li sebelisoa ho sekaseka litšenyehelo tse nyane le chelete e kenang. Ho baeloji, li-derivatives li thusa ho etsa mohlala oa kholo ea baahi le lits'ebetso tsa fisioloji. Boenjiniere, li-derivatives li bohlokoa tlhahlobong ea sebopeho le mechining ea mokelikeli. Saense ea khomphutha e sebelisa li-derivatives ho li-algorithms tsa ntlafatso le ho ithuta ha mochini. K'hemistri, li-derivatives li sebelisoa ho kinetics ea karabelo le thermodynamics. Ka hona, ho utloisisa le ho tseba mohopolo oa li-derivatives ho bohlokoa bakeng sa bo-rasaense le baenjiniere mafapheng a fapaneng.
