MFNWtKUb<ob<R=MDLCdNbobOKr:B[UF`C`=BNSDOED>;EZUVgExwmyxshsYy[Mgjygn?YeCXpKyuciwmyxoeaoG[GWj[tZqFlkhsehrSigQXq=SB;cDWE^_iwmyqKYu[bTOFOOfcEYu_YY;GiocWkfkgHseUaoWfKxpgFgUht[YwDp<Qnxtsi]Xr=TXIWkeXsqpDEuP<QCQlpxRFQu`qt\\YWRYVg=Yt]YxqYyocjwoCaT]DWwCXoFiYHrEe]SG^[glaWlsHlkHs;Yt]YRQfdTOvpn:ET[<RH_dp_llXsLHpDQnw`ToDYkBTQvjeHr<OspKolriexqUROQfFogXyviyt\\Qw[hqHymsps[VgHhhWppMHp@eQ;VC]U^KWjghFaU_mGmwXhWxpLP=UXqMYfMxoePC=UH]Ub?eugdAxnJiudqsUIwFYu`ywmAym?mo@fRpo;`n:qeG`oLgj^`nx`tYPqKixrQyjgns`wkqxp^hPHkehr;WiV@u]iwHaucisVivWwke@Z_?kjFjVhnx`tYOkbtLUUWovgwVh]X`mglcvfSHwiix]rSMNhxQOHqCaQJquZIwkAqEMUHYuauRQ]f[WjE?j[@\\UWiygnp@brOlyPtTAlJxkSGeRwrAyrZNfy?\\PohIiu^y_in_iaxpIxkIxYXqBiho_hjOmghtOitwfavvoAItjfgBXv]YvZwk^XoeXo=Xj<xfaofsHqsXcEOcI@pyXsTAwWhmWpwmyXyTZ`Oxfdron:itYXqLUQ;FpCiuqsWmVvgIxWu_eGF]u^hOyTqG]uATp>IyueyqQyuiwluhQGiO`pGyi]pqBnfB`gMHpCwiZxbxwmlixsQgOXp]gkePfIpo=`o:Ao;It]?liXlkPsyptYQasGm@xnwXtZQwMYvcAvcywZwmn@bwwlQ@qCA^lGle?ml`pDYuDIu]QyuayZ>^Zvt^QwZ^f<xi_`qipsSAaowlexrNYsTav^gkeHsSqvr_nsHvfAxyniV@qJYu:wj[xqMiu]YwlIliHsWPqFA^i_k:GiU@oy`tj^iR@rSIvy_owxwnAyR?kbP]bWkRppEyeL`oKHpDysWqv>it^akdHrAyt^Iu_YwD`o<ajg@rHhoAysZyvtfiUhwlyxFwj]@dNXouxsVQqHyu]glhxfOxoKQvcyyyyyjWacqD@ZnOdHWdyyyyyY:::::::::::::::::::::::::::::::::::::::::J:HouYjL>ZG>gC_b;_drOugYeE^hMfdTnyMp`cOu`hl`Fr>NkP_ot@d:ibNi\\;v]jxfcQbqgalPs\\XkeNn<Wc?QtQOlLqnLOmNNu^x[T?^ZW[eQjN?vrX_hqorpaJvkVv]r_eSGif>v[Gef@[n@t^fcMpns_pCqsuV`MHcT`nJWjAXuMIiVYamwvxwxyywyyiyyaMnmINfv`fgyoYIsEIemXcIvr`Pa=iqcnodnjKfydGq`AkP?upYr:OjswsAwbvveX@yYYf[ouSv]=AovVpLimIn_P`h=AyEntoys;H\\sYyC>ceGj>Wm_qevFpuqlEYv?xbapbpw_yn`Z^rWX[>gnR`hMY^?NvGVqxFapvw=@cuYkKf^vGy?akyF\\AXhi`rwY[SImIq_txy:qrANquNyqoim@_\\qyrG`ZG[IxoLyw=>yhh]uFmJYin_`lXwWPxe?w>xfPWm^wyPvbKiff>ceo`fOmI>xTYkUAfiQskf_J@jNgasNqXnd=HwJ`gtgin>o\\GZPy^gnmyhqOXarXpC>bpNoywxhv[:`^h?fI>sZOaVYxvi]KgxsYvT`kIyc\\Vmu`j<vxayj``gEGp_wowagVYuAHZX@qnwunIwMyrGXwExssX^DW\\nYnT>iiQaSiodYiIaqtwy\\WtxYdmnqr@`cFhjqa]YeIwdhneJqwkaarYqaVcigjR_jo?xVQxaWbnvwugxZypExyjIvVywxY`mayNaqIxxoomXymZOmbOgu?wJI^?PbkosLooDpx;ytnggCpx;GsusXqgTefm?X;=VuaHQmX[yTiciieIaGWy?YiUYQab??brwG>AtyubukgSisKuIsQuT;Y;aRbsRqibByy<EtHWsFqtimsZSe_Yv:[rsYEocwscWeoiXOBi]G^SUaeEy]ItyBYUUE=wcitxeuISeZ?vjiduqIumIoWyKYDnorwWtDID=?h;uC]gS@AIeIiKUVYasSQhdIIrQEcMel]Eh[GCaE@YbA=tWssOusRwyZewcYijYHgsWcqrY=FxKSOgyxkVIgr:?cFKu[sBTAt`IxusbAmr@msLkykqX;aUsGy:Qbh_DnaGaSwEwxhyIwEXUaErWr[uxsaVPuxKmyawXYixxaUKaS^?ExGEXYh@MevcsCauQAHkggsCWHUtH[vfAu:aHfoxRinbPNZPP=Us[ISa<vtQj?<xpYUaql[Tqt`W`ePD`KApJgevADvtXj?@SFIrEyjWtXmXoIHJD`KPdny@PvyRvAQFlYlywqqVmupVTQV@VDtnApr^lmSMlUTVNux>`TWIsSAttPy:=UW\\oMll[TuRUj?lN=`qe<nLmOdppAhXqHTbxkKAr>EujDoUpKFmogmPeDVO=UqqPtUskutQTjkqTCFwTW[x_m`go:fhryp`pl\\Yiu_g@Hl`@whWeaxjdFfx>]u_^kvm\\HkZ``DFncG_lxsyp[lvcB_wof\\xoiXvhe?qaIyXwyVvv?pcwgyLAuFifVQ\\q_\\Ha_`vs@yrox]IqiWnkvV[]wqy_[v?[wimoAtD>cTfphgu>xcxWnm`cE>\\PAbFGq]iuwAcng``xsdQsDoZNYao`h;qh[qexyjBIva@wLH]qa`thuwAi<^q]vmwq[:hZQXe=Y]Mxu^hjZXeEAnf`kg?xMVySO_CYo`hmf?bPFp;Isd@kr@dpwlYAtuh[:Pd_Fc]^gdFmY`ychy?V]tOqjy_:ngJN_pP_iaerivPxtqArL?iSnfVam^AqvW]Tn]iNsuOwiy]FpqA^abwhdykxhyiagV_ggP_bIfxvoPOnD>bTvg[hmZpcHIci@_Hpbd^dAFg:>cffv?`bbybIWwwx]`yy]vx;>juxwfHmvVxmiaDQl_xeowylapZFyWyh;YtnGutxa_ImSvcGYwBQidItVHaQ^iUagAfrmvoFoirfpTn^vA^U_ZaP\\_xxZfmBwdv_aUHxnp\\Xg_lh\\@PeU?o]>co`ewfpmVpHymAoyjQh;^^hHkyghGHpwniZ`h=aqMWg`WoYFqsni]Wge@w?xZDwdHY`QwfwqligsdOj\\X^AoonoakvebqbAvfiAySIcbhb:gpN>ttahNQhGya=nlG@yYFk\\ojM?id@tkVs@vipG[Pnymwv=QxWYJqGnox^kyyMD`GRp[CLYTj=GL?CmEE<[Tm]s]SWOsh[WEnxLnPLJPRPDMd@k=uxDAsdQn^dwf]WuTVNqjWEknTx^=TDuljuUQAvN]U>MVluR?tXmekQ\\rt@L`Up`DKSupceyDIV=Qo]alPPQn\\Oq\\LmmkgHoIakGYl?LkUUWQMvoMQLUU_LmGeYBUn_EkhDp>XXbLTWhs>xugxSKAPtyPpAx>LQ>iNFLklAmq`psesbUJNYu?muvInfDLQXQhLnYhnOmPWxVF<KMlkn@kKITeQuLlNf`lHLvBETaMnUennPSfutVIrv]jY@PjiycuOG]qQPqiHtc\\tKiuHHMqMSg]OSux:HtD<PTdnmQUU<SKHv^TN`LxOUp>xpveQMMUc`U^uu:Qk^ulE@UMxR;pwnEXF]uPpK`xTUQp<`xrlud]LHXRdqRJPwn\\tdtudiRwynXGecQtxHZW>o:_j;o[NYnvId>IZkfdR_rvpuLWug^f<Qp;`_Jig_Fpg@sSgg_?\\Sy_aAtYYxfPkmVuka\\FHtG@k>gj?pc\\VoHNvEFc`WjD@pXIbngtRwjfXmdPiNid_FoBnrZh^W@dJx`yQiOg\\Mnl:XfDOZ@iZRYy<A^`H^:anrXZGHe=nn>qd^gxe@xjvhSWk@wlFwbOgx\\xmaAyJF]NPgFHyJ?bLF^uGacf_nGu[P\\MwopyhiFhsWwv_sQqhW?meQfPNdlNkWvpMOs`?nY?be?vJAflNpQxna?lqWfIag;?dcGski\\rHfSF\\]NflPxLQiBYb?`nMnjgW_mW[lQhmAy;obK>[EigTG_aa\\;NtJ^y[^\\kohQ@uSfaTI[i^kQF\\;AqG@ehinUHr?PsKOpUOqh^\\NFcJwhf@nSYisVuAW\\?YbgvpjxvHorKwj;Qvk>eJGh;fgx`tfNaHHgJ@pkNlnIZYH_:pa`Ax=hlZHsKfbrFyDpoZXp]_o\\>myVn^IgJg`FVymn_@^_cxi\\Or[fe;Os?Akhp]ZWcZF\\afv;Fo`^hMP\\O^ohOu>ohAFqR?`Fnt=Ytty<MUVcEuYI=[s;mtQSXxshLWuVwH@ov>GWnsb?uI`od]MS=MTQAh<CDESrbYV<GgLsXQGhSsEAobqebR_Tq=WRmTTeFwAEn[FkWXWGiT_TVsfdcfJ_WMSTKEfKWUACX_[CA?im=TWEC?IblSYr;ihQdeOCDCh=Cx__fS]vGkF]qUewDUqcC[FCevKoxhybOUSksEEscO[drKDtsgx]vNYUYMwq;yHERXsdAEVhosb?VcGGWyxkSIRaHreHLYElMeQArbSRkUVOeDGidSMDDWfiaYn=XRMVd=x]EElGg[_UIUWWAH<uVq=BwkG@Cfu=bD?RdatFuT=IDpgRZqcwAhV[SmSSOgx^OXpOuoUrM;UmCsvWDB?sCCVdwHsESvgXlKbPkBmcCWITcCfyKcLKHFove[FDih=it=Ues;XXIDbkIikgFoIBkraUU\\kYNwu[Ky=kX_=fE_RgcVCiHDQiN[DPUVH]r?crTkWTCeR;eGMV^=u<mVX?SyWGYCxnMT;?dj;cc?IvkXsORSKeTAc_gRWQvSkr:SruQwl;FPaGbOfGeYZSStGEE;F==UDEWBGXbwJkMNiDVHuOduodIlWpriXXnlUYMsNqpt@N\\av@hNHPr\\aKS]tnLJNpLfLY;YKL\\TPTqs@S[lRt]psETdeKcEvMQjjeT=`luDRa\\lPajKyqmHn@`xt=YBHPdhkOdW\\XWD]j@MrOxokdj_\\xAMj;]Qk`O>\\OKtLKinOXS;MLxhmE]SFmy:AU@]n;Lwt@V\\]niTW;QwqXugLO^ewZ`kq@MuUkbMVR]XeLwhTwDQjFPoYyS`Dq[el><QjlwvDRBPnB\\s@uNA\\tnpTZYS?uv`dv_]RRQm@tTwPJnEPdaux]UGXMJinNeLnYjSPJNmqtxt<Pq]Mk=YpvYTl]Ji@TrLNRilU=UNyQmeOceun=KuaU@]NkeP<MNvDseIkQINglXKlWrqpD<TLLTQXMVYS[EVREt:QpZ@pjmKIqlHEt`MXG=OLLQrTtxLTl=vDdsD@r`iLTmJMmsnMVMqV>qTlPKNPWkLmnMTaDTSpxl\\k<Tw;iNkDJPHnAdWYmWb@KAIktuJ_tWJaNmeqFiJEesGatWHMrLmFuRitXAYOpXmjLO\\DvkmqQ@oNPwf]NOElEtU\\<wZUnddnL`pPQU;mUZdJ`dsrpuEuWNAYjaoudoNLQnAU:MS?]qJlvUpy@`J><pBhph=Wi]SrxOZ]j;<wE@NJtKjlOcELThV`<lBdW?\\Mn<P_QLTqV\\YK=AkQMMM`svlVyDty=r:ujOTX?xKyDslYL?hLwyr;EKLAVh<ytpj_`q[`jq<VWAjoUJPiKR]p\\=VwqOHMO_qoa]u=Ilo]tktWemPjLoA]r:YtEXmOhOd\\KLusrxj]<vkIPiUpkAMOIl:QWlAyrAqELRHPlkylUiSOxorXTtLPjykgiKeUO[dxFDRvanOyVcett]mkXWgLX`mpDAN>pNvYwVDnXyRW]N[uYu\\TA\\rMXm;qjquM^iw;DTg=xlaJ?]v:TlkAJALmu<kxUMtisS\\tIYJrqMI`kButt]QCaR<ArXmnDUwWIR>tThQsruklduFXw=pjYpwiptLLRk`k[equTTthu>yPAmqrDPxET=hNw<R[Iy\\LvCqprmMgdM:Il@EN\\\\NqMLs<RJEukyXCqJaMQkImBtMLYQT<ohXQeLYPAvQ\\XP]ofQnNHr<yn\\uNIEkIeU<]qoYOlxNsYoC`oLeKbTjh@TIEKs\\NsXjWHTDaTTIs>djiPNVdsd`SeIxa\\pBdyJ@YDMmPALJeMxys_LNnDMGmQa]lEySFyvg=VPAt<pTe=UW]PApk\\`nvEoByKEMmZQNrlmnpRk\\TIqXQ=nOMo:pj[xqMAWfYoJtLl`TeHrUUMKasRQY<TXwemc=v<yt_AUb@kapqCEva=oV\\rqmUSLW;AlCdun`JO`YuTqlqs;lXxUUfEVyQUAaTwHu?QlPPV:QptLNREO<pMmHNZmSqtq<xvg]Tphs\\MW[ayYdWexOyiVD]yd=J:<J:`n\\tN\\tT[<P;;:::4:\"\{\}-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"%S@F*-%.BOUNDS_HEIGHTG6#$"$g)F*-%)CHILDRENG6"Guia de Estudo de C\303\241lculo\302\251 Maplesoft, a division of Waterloo Maple Inc., 2005Cap\303\255tulo 14: Deriva\303\247\303\243o Impl\303\255cita
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field>Muitas curvas interessantes n\303\243o podem ser escritas na forma expl\303\255cita 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 mas podem ser dadas na forma impl\303\255cita LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYmLUYsNiVRInhGJ0Y2RjktRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GT0ZRL0ZVUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZhcC1JI21uR0YkNiRRIjBGJ0ZARkBGK0ZASabemos que a inclina\303\247\303\243o (slope) da reta tangente (line tangent) a uma curva (curve) em um ponto \303\251 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 e, agora, estamos confort\303\241veis, encontrando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUkmbWZyYWNHRiQ2KC1GIzYkLUYsNiVRI2R5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y9USdub3JtYWxGJy1GIzYkLUYsNiVRI2R4RidGOUY8Rj8vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRksvJSliZXZlbGxlZEdRJmZhbHNlRictSSNtb0dGJDYtUSI9RidGPy8lJmZlbmNlR0ZQLyUqc2VwYXJhdG9yR0ZQLyUpc3RyZXRjaHlHRlAvJSpzeW1tZXRyaWNHRlAvJShsYXJnZW9wR0ZQLyUubW92YWJsZWxpbWl0c0dGUC8lJ2FjY2VudEdGUC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRl9vLUYjNictRiw2JVEkZn4nRidGOUY8LUZSNi1RMCZBcHBseUZ1bmN0aW9uO0YnRj9GVUZXRllGZW5GZ25GaW5GW28vRl5vUSYwLjBlbUYnL0Zhb0ZbcC1GIzYmLUZSNi1RIihGJ0Y/L0ZWRjtGVy9GWkY7RmVuRmduRmluRltvL0Zeb1EsMC4xNjY2NjY3ZW1GJy9GYW9GZXAtRiM2JC1GLDYlUSJ4RidGOUY8Rj8tRlI2LVEiKUYnRj9GYnBGV0ZjcEZlbkZnbkZpbkZbb0ZkcC9GYW9RLDAuMTExMTExMWVtRidGP0YrRj9GK0Y/RitGPw== para fun\303\247\303\265es expl\303\255citas (explicitfunctions). Deriva\303\247\303\243o Impl\303\255cita (Implicitdifferentiation) \303\251 uma t\303\251cnica que pode ser usada para encontrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEjZHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjtRJ25vcm1hbEYnLUYjNiQtRiw2JVEjZHhGJ0Y3RjpGPS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGSS8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrRj0= quando a fun\303\247\303\243o \303\251 dada implicitamente (implicitly). \303\211 essencialmente a regra da cadeia aplicada \303\240 identidade 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Como isto \303\251 realmente uma aplica\303\247\303\243o da derivada, este cap\303\255tulo consiste principalmente de exemplos. O primeiro exemplo examina um c\303\255rculo ( circle) por ambas as formula\303\247\303\265es, uma expl\303\255cita (explicit) e outra impl\303\255cita. O segundo exemplo examina uma fun\303\247\303\243o realmente impl\303\255cita, o Folium de Descartes. O \303\272ltimo exemplo estende a Regra de Pot\303\252ncia (Power Rule) a todos os expoentes racionais (rationalexponents).O TangentLinePlot maplet (o Tangents Tutor incorporado) pode ser usado para auxiliar com a vizualiza\303\247\303\243o das retas tangentes (tangent) ao gr\303\241fico (graph) de uma fun\303\247\303\243o impl\303\255cita definida.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Gloss\303\241rio</Font></Text-field>Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio de Matem\303\241tica Maple ( Maple Math Dictionary).
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Inicializa\303\247\303\243o</Font></Text-field>restart;
with( plots ):
with( Student[Calculus1] ):
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 14.1: <Hyperlink linktarget="Dictionary:Definition,tangent" hyperlink="true"><Font style="Heading 1" encoding="UTF-8">Retas Tangentes a um C\303\255rculo</Font></Hyperlink></Text-field>O c\303\255rculo centrado na origem (origin) e tendo raio (radius) 3 pode ser descrito como o conjunto (set) de todos os pontos que satisfazemq1 := x^2 + y^2 = 9:
q1;Seja LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= um n\303\272mero com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEiM0YnRi8tRiw2LVEiPEYnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRkotRkc2JFEjMy5GJ0YvLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjIyMjIyMmVtRicvRkVGZ25GLw== Porque ambos, 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 e 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 , est\303\243o sobre o gr\303\241fico do c\303\255rculo, a equa\303\247\303\243o para o c\303\255rculo n\303\243o \303\251 uma fun\303\247\303\243o. (Lembre que ela define uma rela\303\247\303\243o.) Figura 14.1 fornece um gr\303\241fico para este c\303\255rculo, obtido no Maple via o comando implicitplot.
implicitplot(q1, x=-4..4, y=-4..4, scaling=constrained);Figura 14.1 Gr\303\241fico do c\303\255rculo 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
A determina\303\247\303\243o da inclina\303\247\303\243o da reta tangente ao c\303\255rculo no 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 sobre o c\303\255rculo requer que encontremos 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 . A id\303\251ia por tr\303\241s da deriva\303\247\303\243o impl\303\255cita \303\251 pensar na equa\303\247\303\243o do c\303\255rculo como defini\303\247\303\243o impl\303\255cita de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= como uma fun\303\247\303\243o de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= . Isto significa que precisamos substituir todas as ocorr\303\252ncias de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== tal que a equa\303\247\303\243o do c\303\255rculo fiqueyimpl := y=y(x):
yexpl := y(x)=y:
q2 := eval( q1, yimpl );Agora, ambos os lados desta identidade s\303\243o derivados (differentiated) em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, levando aq3 := diff(q2, x):
q3;Note o uso da Regra da Cadeia (Chain Rule) para computar 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.Agora \303\251 uma simples quest\303\243o de resolver uma outra derivada, cujo resultado \303\251q4 := isolate( q3, diff(y(x),x) ):
q4;Para colocar este resultado em uma forma consistente com a equa\303\247\303\243o original, substitua todas as ocorr\303\252ncias de 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 por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= de modo que a derivada (derivative) seja dada por
q5 := dy/dx = eval( rhs(q4), yexpl):
q5;(14.1)
Por exemplo, a inclina\303\247\303\243o da reta tangente ao c\303\255rculo no ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkktRiM2Ji1GMjYtUSIoRidGNS9GOVEldHJ1ZUYnRjsvRj5GUkY/RkFGQ0ZFL0ZIUSwwLjE2NjY2NjdlbUYnL0ZLRlUtRiM2Jy1JI21uR0YkNiRRIjJGJ0Y1LUYyNi1RIixGJ0Y1RjgvRjxGUkY9Rj9GQUZDRkVGRy9GS1EsMC4zMzMzMzMzZW1GJy1JJm1zcXJ0R0YkNiMtRlo2JFEiNUYnRjVGK0Y1LUYyNi1RIilGJ0Y1RlFGO0ZTRj9GQUZDRkVGVC9GS1EsMC4xMTExMTExZW1GJ0Y1RitGNUYrRjU= \303\251eval(q5, [x=2, y=sqrt(5)]);enquanto que, no pontoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkktRiM2Ji1GMjYtUSIoRidGNS9GOVEldHJ1ZUYnRjsvRj5GUkY/RkFGQ0ZFL0ZIUSwwLjE2NjY2NjdlbUYnL0ZLRlUtRiM2Jy1JI21uR0YkNiRRIjJGJ0Y1LUYyNi1RIixGJ0Y1RjgvRjxGUkY9Rj9GQUZDRkVGRy9GS1EsMC4zMzMzMzMzZW1GJy1GIzYmLUYyNi1RKiZ1bWludXMwO0YnRjVGOEY7Rj1GP0ZBRkNGRUZHRkotSSZtc3FydEdGJDYjLUZaNiRRIjVGJ0Y1RitGNUYrRjUtRjI2LVEiKUYnRjVGUUY7RlNGP0ZBRkNGRUZUL0ZLUSwwLjExMTExMTFlbUYnRjVGK0Y1RitGNQ==, a inclina\303\247\303\243o da reta tangente ao c\303\255rculo \303\251eval(q5, [x=2, y=-sqrt(5)]);Que outros m\303\251todos poder\303\255amos usar para encontrar estas inclina\303\247\303\265es?As partes superior e inferior do c\303\255rculo s\303\243o, separadamente, gr\303\241ficos das fun\303\247\303\265es expl\303\255citaseq[top] := sqrt( 9 - x^2 ):
eq[bot] := -sqrt( 9 - x^2 ):
y[top] = eq[top];
y[bot] = eq[bot];As inclina\303\247\303\265es nos pontos da metade superior e da metade inferior podem ser encontradas derivando estas express\303\265es. Infelizmente, n\303\243o sabemos ainda como derivar a fun\303\247\303\243o raiz (root) quadrada. (At\303\251 o presente, a Regra de Pot\303\252ncia se aplica somente quando o expoente \303\251 um inteiro.) Mas, deixando o Maple computar estas derivadas por n\303\263s, a inclina\303\247\303\243o da reta tangente em um ponto da metade superior do c\303\255rculo encontrada \303\251d1 := diff( eq[top], x ):
dy/dx = d1;A corre\303\247\303\243o deste resultado pode ser checada usando (14.1) e a equa\303\247\303\243o para a parte superior do c\303\255rculo, a saber,eval( q5, y=eq[top] );Do mesmo modo, a inclina\303\247\303\243o da reta tangente em um ponto da metade inferior do c\303\255rculo \303\251d2 := diff( eq[bot], x ):
dy/dx = d2;a qual concorda comeval( q5, y=eq[bot] );o resultado de (14.1).A express\303\243o para a derivada em (14.1) \303\251 definida somente se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+Rj5GK0Y+. Isto faz sentido porque LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiM0YnRj5GPkYrRj4= ou 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 e neste pontos as retas tangentes s\303\243o verticais. Estas caracter\303\255sticas, junto com as duas retas tangentes ao c\303\255rculo nos pontos onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMkYnRj5GPkYrRj4= , s\303\243o evidentes na Figura 14.2.
p1 := Tangent( eq[top], x=2, -4..4, output=plot,
functionoptions=[color=red, legend=["Top of circle"]],
tangentoptions=[color=gold,legend="Tangent (top)"] ):
p2 := Tangent( eq[bot], x=2, -4..4, output=plot,
functionoptions=[color=blue, legend=["Bottom of circle"]],
tangentoptions=[color=green,legend="Tangent (bottom)"] ):
display( [p1,p2], view=[-4..4,-4..4], title="" );Figura 14.2 O c\303\255rculo na Figura 14.1, junto com as duas retas tangentes em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 14.2: Folium de Descartes</Text-field>A forma geral para o Folium de Descartes \303\251 dada pela equa\303\247\303\243o impl\303\255citar1 := x^3 + y^3 = 3*a*x*y;onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um par\303\242metro (parameter).
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Visualizando o Folium de Descartes</Text-field>Antes de analisar estas curvas ser\303\241 bom ter uma id\303\251ia da apar\303\252ncia destas curvas. A Figura 14.3 fornece uma amostra de anima\303\247\303\243o gr\303\241fica do Folium de Descartes para valores (values) inteiros de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= deLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEiM0YnRi9GLw== a 3.
display([seq( implicitplot( r1, x=-6..6, y=-6..6, numpoints=2000,
title=sprintf("Folium of Descartes: a = %a",a) ),
a=-3..3 )], insequence=true);Figura 14.3 Folium de Descartes para inteiros 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
Para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=, o Folium se degenera na reta 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. Para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+LUY7Ni1RIixGJ0Y+RkBGQ0ZFRkdGSUZLRk1GT0ZSRj5GK0Y+ as curvas s\303\243o mais interessantes. Em particular, existem regi\303\265es onde existem tr\303\252s pontos sobre a curva para um \303\272nico valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= . (Iste \303\251 de se esperar porque toda equa\303\247\303\243o c\303\272bica com coeficientes reais (real-valued) tem tr\303\252s ra\303\255zes reais ou complexas (complex roots) --- e ra\303\255zes complexas aparecem em pares conjugados.)
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Encontrando a Inclina\303\247\303\243o por Deriva\303\247\303\243o Impl\303\255cita </Font></Text-field>Deriva\303\247\303\243o impl\303\255cita ser\303\241 usada para encontrar a inclina\303\247\303\243o da reta tangente em cada ponto sobre o Folium de Descartes. Para este fim, substitua cada letra LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= por 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 para obterr2 := eval( r1, yimpl ):
r2;E, ent\303\243o, use a regra da cadeia (chain rule) para derivar em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ambos os lados desta identidade, obtendor3 := diff( r2, x ):
r3;Resolvendo para a nova derivada d\303\241 r4 := simplify(isolate( r3, diff(y(x),x) )):
r4;Substituindo 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 pelo simples LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, coloca a derivada na forma r5 := dy/dx = eval(rhs(r4),yexpl):
r5;N\303\243o nos surpreende que uma ferramenta t\303\243o poderosa como o Maple tenha um comando embutido para calcular derivadas impl\303\255citas. Seu uso aqui leva \303\240 seguinte derivada.implicitdiff(r1,y,x);
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Pontos sobre a Curva com Tangentes Horizontais </Text-field>Esta informa\303\247\303\243o pode ser usada para identificar alguns pontos especiais sobre estas curvas. Por exemplo, a reta tangente \303\240 curva \303\251 horizontal nos pontos sobre a curva onde a inclina\303\247\303\243o \303\251 zero, i.e., nos 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 que satisfazem (satisfy) ambas as seguintes equa\303\247\303\265es.r1;
r6 := numer( rhs(r5) ) = 0:
r6;Maple informa as solu\303\247\303\265es (solutions) deste par de equa\303\247\303\265es comor7 := [solve( {r1,r6}, {x,y} )];A nota\303\247\303\243o RootOf \303\251 o modo de o Maple listar concisamente todas as ra\303\255zes reais e complexas de um polin\303\264mio (polynomial). Podemos for\303\247ar a expans\303\243o total das solu\303\247\303\265es com o comando allvalues (allvalues) . O resultado \303\251r8 := map(allvalues,r7);Somente as solu\303\247\303\265es reais s\303\243o de interesse para n\303\263s; por isso removemos (remove) todas as solu\303\247\303\265es que tenham partes imagin\303\241rias:r9 := remove( has, evalc(r8), I );Isto leva, para cada valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+Rj5GK0Y+ , a dois pontos com tangentes horizontais, a saber, os pontosseq( eval( [x,y], S ), S=r9 );
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Pontos Sobre a Curva com Tangentes Verticais </Text-field>Pelo mesmo motivo, a inclina\303\247\303\243o da reta tangente \303\240 curva \303\251 indefinida nos pontos que satisfazem a duas condi\303\247\303\265esr1;
r10 := denom(rhs(r5)) = 0:
r10;As solu\303\247\303\265es reais encontradas, deste sistema, s\303\243or11 := [solve( {r1,r10}, {x,y} )]:
r12 := map(allvalues,r11):
r13 := remove( has, evalc(r12), I ):
seq( eval( [x,y], S ), S=r13 );Note que a origem tem ambas as retas tangentes, uma horizontal e uma vertical, e que os outros pontos s\303\243o sim\303\251tricos (symmetric) em rela\303\247\303\243o \303\240 reta LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInhGJ0Y0RjdGPkYrRj4= . (Um exame mais de perto na equa\303\247\303\243o original e na f\303\263mula para a inclina\303\247\303\243o explica a causa disto, e de outras simetrias, eram de se esperar.)
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Pontos Sobre a Curva com <Equation executable="false" style="2D Math_16" input-equation="" display="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">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</Equation> </Text-field>Pontos onde a inclina\303\247\303\243o da reta tangente \303\251 1 s\303\243o solu\303\247\303\265es para as equa\303\247\303\265esr1;
r14 := rhs(r5) = 1:
r14;As solu\303\247\303\265es reais encontradas para este sistema s\303\243or15 := [solve( {r1,r14}, {x,y} )]:
r16 := map(allvalues,r15):
r17 := remove( has, evalc(r16), I ):
seq( eval( [x,y], S ), S=r17 );ou com aproxima\303\247\303\265es do ponto de futua\303\247\303\243o (floating-point) para raizes quadradasseq( eval( [x,y], evalf(S) ), S=r17 );Novamente, note a simetria nestas solu\303\247\303\265es. Note tamb\303\251m que estas solu\303\247\303\265es n\303\243o s\303\243o corretas para r LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=. Que n\303\243o existem pontos sobre o gr\303\241fico com inclina\303\247\303\243o 1 quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= pode ser visto da janela na anima\303\247\303\243o com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= assim como da rsposta do Maple para o seguinte comando.[solve( eval( {r1,r14}, a=0 ), {x,y} )];
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Coment\303\241rios de Conclus\303\243o: Forma Expl\303\255cita para Folium de Descartes </Font></Text-field>No in\303\255cio deste exemplo, estava implicado que n\303\243o era poss\303\255vel encontrar uma representa\303\247\303\243o expl\303\255cita para o Folium de Descartes. Como tamb\303\251m \303\251 verdade que cada Folium n\303\243o \303\251 o gr\303\241fico de uma fun\303\247\303\243o; \303\251 poss\303\255vel encontrar uma f\303\263rmula expl\303\255cita para cada segmento da curva.r18 := [solve( r1, {y} )]:
for S in r18 do
op(S)
end do;A primeira das tr\303\252s solu\303\247\303\265es \303\251 sempre real. As outras duas ou s\303\243o reais ou complexos conjugados; quando elas s\303\243o reais o Folium tem tr\303\252s pontos para um \303\272nico valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Quando elas s\303\243o complexos conjugados (complex conjugates) existe somente um ponto sobre a curva para cada valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=; e na transi\303\247\303\243o entre estes estados -- o \303\272nico valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= com dois pontos sobre a curva -- estas duas solu\303\247\303\265es se reduzem a uma \303\272nica solu\303\247\303\243o repetida.Mesmo se pud\303\251ssemos decidir qual dessas tr\303\252s f\303\263rmulas usar, as derivadas seriam pribitivamente complicadas. Por compara\303\247\303\243o, computa\303\247\303\243o da derivada pela deriva\303\247\303\243o impl\303\255cita foi quase sem esfor\303\247o.Quest\303\243o 14.1LywqKipJKUVuY29udHJlRzYiIiIiSSNkeEdGJkYnSSNkeUdGJiEiIkklcGFyYUdGJkYnRicqJEkieEdGJiIiIyEiJyokSSN4eUdGJiIiJUYqSSJ5R0YmIiInIiIhQuest\303\243o 14.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(Nota: Voc\303\252 deve digitar uma resposta antes de clicar em "Grade".)
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Exemplo 14.3: A Regra de Pot\303\252ncia para Expoentes Racionais </Font></Text-field>No Exemplo 14.1 (trabalhando sem Maple), fomos incapazes de encontrar a inclina\303\247\303\243o da reta tangente em um ponto sobre a parte superior ou inferior de um c\303\255rculo, porque n\303\243o sab\303\255amos como derivar a fun\303\247\303\243o raiz quadrada. No entanto poder\303\255amos ter derivado este resultado para a fun\303\247\303\243o raiz quadrada usando a defini\303\247\303\243o de derivada; \303\251 muito mais eficiente e \303\272til manusear todos os expoentes racionais simultaneamente. Neste exemplo a deriva\303\247\303\243o impl\303\255cita ser\303\241 usada para mostrar que a Regra de Pot\303\252ncia se aplica para todos os expoentes racionais. Mostraremos que , se 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 com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= inteiros e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+Rj5GK0Y+, ent\303\243oLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSNkeEYnRjdGOkY9LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZJLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGPQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJuRidGNUY4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrL0Y5USdub3JtYWxGJw== = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZRLUklbXN1cEdGJDYlLUYsNiVRInhGJ0Y0RjctRiM2JkYrLUYjNiZGMS1GOzYtUSgmbWludXM7RidGPkZARkNGRUZHRklGS0ZNRk9GUi1JI21uR0YkNiRRIjFGJ0Y+Rj5GK0Y+LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRj5GK0Y+A chave para converter a forma expl\303\255citas1 := y = x^n:
s1;em representa\303\247\303\243o impl\303\255cita com expoentes inteiross2 := y^q = x^p:
s2;Para preparar para a deriva\303\247\303\243o impl\303\255cita, lembremo-nos (e ao Maple) de que 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. A equa\303\247\303\243o definida \303\251, portanto,s3 := eval( s2, yimpl ):
s3;A deriva\303\247\303\243o de ambos os lados da equa\303\247\303\243o em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= d\303\241s4 := diff( s3, x ):
s4;Resolvendo para a outra derivada temoss5 := isolate( s4, diff( y(x), x ) ):
s6 := dy/dx = simplify( eval(rhs(s5),yexpl) ) assuming p::integer, q::integer;Gostar\303\255amos de expressar esta derivada em termos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. A rela\303\247\303\243o expl\303\255cita LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUklbXN1cEdGJDYlLUYsNiVRInhGJ0Y0RjctRiw2JVEibkYnRjRGNy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y+RitGPg== com 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 (logo 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 ) permite que a derivada seja reescrita comoqs := simplify( eval( s6, [s1,p=n*q] ) ) assuming q::integer:
qs;Isto conclui a prova (proof) de que a Regra de Pot\303\252ncia se aplica para todos os expoentes racionais. Quest\303\243o 14.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
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Resumo</Font></Text-field>Dado que 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 \303\251 definido implicitamente pela equa\303\247\303\243o 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, a deriva\303\247\303\243o impl\303\255cita \303\251 uma t\303\251cnica para 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 , a inclina\303\247\303\243o da reta tangente \303\240 curva. A chave para usar deriva\303\247\303\243o impl\303\255cita com sucesso \303\251 lembrar que uma vari\303\241vel (variable) \303\251 definida implicitamente em termos da outra, usualmente 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, e que a deriva\303\247\303\243o em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= de qualquer termo envolvendo 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 envolver\303\241 automaticamente a Regra da Cadeia.Uma express\303\243o para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEjZHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjtRJ25vcm1hbEYnLUYjNiQtRiw2JVEjZHhGJ0Y3RjpGPS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGSS8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrRj0= obtida pela deriva\303\247\303\243o impl\303\255cita envolver\303\241 tipicamente ambos, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Os Exemplos 14.1 e 14.2 demonstram como esta forma para a derivada pode ser usada efetivamente. O exemplo final estende a Regra de Pot\303\252ncia de expoentes inteiros para expoentes racionais. Deriva\303\247\303\243o impl\303\255cita ser\303\241 usada no Cap\303\255tulo 15 sobre (????) Related Rates.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Qual \303\251 o Pr\303\263ximo?</Font></Text-field>Este conclui aUnidade 2. Voc\303\252 agora conhece as t\303\251cnicas necess\303\241rias para derivar v\303\241rias classes de fun\303\247\303\265es. voc\303\252 pode tamb\303\251m entender a conex\303\243o entre derivada, varia\303\247\303\243o (instant\303\242nea) e a inclin\303\247\303\243o de uma reta tangente a uma curva. Na Unidade 3, usaremos as id\303\251ias introduzidas nesta unidade em um n\303\272mero de aplica\303\247\303\265es.Chapter Navigation<< Prev12345678910111213 14 1516171819202122232425262728293031Next >>
Table of Contents\302\251 Maplesoft, a division of Waterloo Maple Inc., 2005. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com