资源描述：
《ImplicitandExplicitFunctions隐函数》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Differentiation2ImplicitDifferentiation2.5ImplicitandExplicitFunctionsImplicitandExplicitFunctionsMostfunctionshavebeenexpressedinexplicitform.Forexample,intheequationthevariableyisexplicitlywrittenasafunctionofx.Somefunctions,however,areonlyimpliedbyanequat
2、ion.Forinstance,thefunctiony=1/xisdefinedimplicitlybytheequationxy=1.ExplicitformSupposeyouwereaskedtofinddy/dxforthisequation.Youcouldbeginbywritingyexplicitlyasafunctionofxandthendifferentiating.Thisstrategyworkswheneveryoucansolveforthefunctionexplicitly.
3、Youcannot,however,usethisprocedurewhenyouareunabletosolveforyasafunctionofx.ImplicitandExplicitFunctionsSupposeyouwereaskedtofinddy/dxforthisequation.Youcouldbeginbywritingyexplicitlyasafunctionofxandthendifferentiating.Thisstrategyworkswheneveryoucansolvefo
4、rthefunctionexplicitly.Youcannot,however,usethisprocedurewhenyouareunabletosolveforyasafunctionofx.ImplicitandExplicitFunctionsSupposeyouwereaskedtofinddy/dxforthisequation.Youcouldbeginbywritingyexplicitlyasafunctionofxandthendifferentiating.Thisstrategywor
5、kswheneveryoucansolveforthefunctionexplicitly.Youcannot,however,usethisprocedurewhenyouareunabletosolveforyasafunctionofx.ImplicitandExplicitFunctionsSupposeyouwereaskedtofinddy/dxforthisequation.Youcouldbeginbywritingyexplicitlyasafunctionofxandthendifferen
6、tiating.Thisstrategyworkswheneveryoucansolveforthefunctionexplicitly.Youcannot,however,usethisprocedurewhenyouareunabletosolveforyasafunctionofx.ImplicitandExplicitFunctionsForinstance,howwouldyoufinddy/dxfortheequationwhereitisverydifficulttoexpressyasafunc
7、tionofxexplicitly?Todothis,youcanuseimplicitdifferentiation.ImplicitandExplicitFunctionsTounderstandhowtofinddy/dximplicitly,youmustrealizethatthedifferentiationistakingplacewithrespecttox.Thismeansthatwhenyoudifferentiatetermsinvolvingxalone,youcandifferent
8、iateasusual.However,whenyoudifferentiatetermsinvolvingy,youmustapplytheChainRule,becauseyouareassumingthatyisdefinedimplicitlyasadifferentiablefunctionofx.ImplicitandExplicitFunctionsExample1–Di
