**TI83F* 06/25/03, 14:55 DERIVTX  GWju!,a Q!`@bg>=  Derivatives (Text)David Dude6/25/2003 v.1.1dude@dudefree.comcd(c)=P0P'u^nnd(u)=Pn-1nuduPcud(cu)=PcduP "u +/- vd(u+/-v)=Pdu+/-dvPuvd(uv)=Pvdu+udvP0u/vud(---)=vPvdu-udv---------vP sin ud(sinu)=PcosuduP cos ud(cosu)=P-sinuduP tan ud(tanu)=PsecuduP cot ud(cotu)=P-cscuduP sec ud(secu)=PsecutanuduP csc ud(cscu)=P-cscucotuduP'e^uud(e)=PueduP ln ud(lnu)=Pdu--uP,a^uud(a)=PualnaduP 0loga ud(logu)=aP1du-----lnauP sin ud(sinu)=Pdu-------(1-u)P cos ud(cosu)=P-du-------(1-u)P tan ud(tanu)=Pdu-----1+uP cot ud(cotu)=P-du-----1+uP sec ud(secu)=Pdu---------|u|(u-1)P csc ud(cscu)=P-du---------|u|(u-1)P4Def (h form)DefinitionofDerivative:Pf(x+h)-f(x)lim-----------h->0hPDDef (c form)DefinitionofDerivativeataPoint:Pf(x)-f(c)lim---------x->cx-cP1ChainRuled--f(g(x))=dxPf'(g(x))g'(x)PHDeriv FailsWheremightthederivativefailtoexist:P*cornerorcusp*verticaltangent*discontinuityP ;vel posVelocityisthederivativeof...PpositionP ?acc velAccelerationisthederivativeof...Pvelocity(andthesecondderivativeofposition)P %JerkWhat'sa"jerk"???PJerkisthederivativeofacceleration.Ifabody'spositionattimetiss(t),thebody'sjerkattimetis#dads*j(t)=--=---1dtdtPSource:Calculus:Graphical,Numerical,Algebraic,Finney,et.al,p.137,(c)2003PearsonEducation]P'CriticalPtCriticalPointPApointwherethefirstderivativeis0ordoesnotexist.P/PointOfInflecPointofInflectionPApointwherethefunctionchangesconcavity.P,MeanValThmMeanValueTheorem:Pf(b)-f(a)f'(c)=---------b-aP*NewtonsMethNewton'sMethod:Pf(x)nx=x-------n+1nf'(x)#nP(