6.2Differentiation A-level考试纯数学P1课件.pptVIP

Chapter6Differentiation

Thegradientformulaforquadraticgraphsy=x2y=ax2y=bx+cy=ax2+bx+cy=2xy=2axy=by=2ax+b

SomenewnotationLettheequationofacurvebey=f(x).Thenthegradientformulaisdenotedbyf’(x).Thisispronounced‘fdashedx’.Theprocessoffindingthegradientofthetangenttoacurveiscalleddifferentiation.Whenyoufindthegradientformula,youaredifferentiating.Thequantityf’(2)iscalledthederivativeoff(x)atx=2

ExampleDifferentiatey=3x2–2x+5Findtheequationsofthetangentandthenormaltothegraphofy=3x2-2x+5atthepointforwhichx=1

ExampleDifferentiate(a)f(x)=2(x2–3x–2),(b)g(x)=(x+2)(2x–3)

ExampleFindtheequationofthetangenttothegraphofy=x2–4x+2whichisparalleltothex-axis

SomerulesfordifferentiationIff(x)=ax2+bx+c,thenf(x)=2ax+bIfyouaddtwofunctions,thederivativeofthesumisthesumofthederivatives:iff(x)=g(x)+h(x),thenf’(x)=g’(x)+h’(x).Ifyoumultiplyafunctionbyaconstant,youmultiplyitsderivativebythesameconstant:iff(x)=ag(x),thenf’(x)=ag’(x).

Iff(x)=xn,wherenisarationalnumber,thenf’(x)=nxn-1

ExampleFindtheequationofthetangenttothegraphofatthepointwherex=9

ExampleDifferentiateeachofthefunctionsx(1+x2)

ExampleFindtheequationofthetangenttothegraphofatthepoint(8,2).