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HereareabunchofderivativesyoushouldprobablyknowTocomputethederivativesofallpolynomials,we’dneedtoknowthederivativesofxnforhighern Chapterwillemphasizewhatderivativesare,Here,werepresentthederivativeofafunctionbyaprimesymbol.Let’sstartwithanexample:dDerivatives.For example,writingB′:T;representsthederivativeofthefunctionBevaluatedatpointTSimilarly,writingE2′indicateswearecarryingoutthederivativeofthe functionETheprimeWewillgetadefinitionforthederivativeofafunctionandcalculatethederivativesofsomefunctionsusingthisdefinitionfunction:f(x) derivative:f0(x)xa~freiwald/Math/Inthetablebelow,?TableofderivativesIntroductionThisleafletprovidesatableofcommonfunctionsandtheir derivativesThetableofderivativesy=f(x)dydx=f′(x)k,anyconstantxTitleCalculusCheatSheetAllAuthorptdawCreatedDate/9/AMTitle: CalculusCheatSheetAllAuthor:ptdawCreatedDate/9/AMOkay,soweknowthederivativesofconstants,ofx,andofx2,andwecanusethese(together withthelinearityofthederivative)tocomputederivativesoflinearandquadraticfunctions.Inthislecture,wewanttounder-standderivatives,seesomerelatively easywaystocalculatethederivatives,andbegintolookatsomewayswecanusederivatives.Wehighlyrecommendpracticingwiththem(orcreatingashcards forthem)andlookingatthemoccasionallyuntiltheyareburnedintoyourmemoryTABLEOFDERIVATIVESFUNCTIONDERIVATIVECcxcxaaxsinx cosxcosxsinxtanx(secx)2secxsecxtanxexelnjxjxax(lna)axlogbx(lnb)xsinhxcoshxcoshxThefunctionwhichtakesthederivativeatagivenpointiscalledthe derivativefunctionWenowbegintocomputederivativesofmorecomplicatedfunctionsbuiltfromcombinationsofsimplerfunctionsDerivativeFormulasThen wewillexaminesomeofthepropertiesofderivatives,seesomerelativelyeasywaystocalculatethederivatives,andbegintolookatsomewayswecanuse derivativesSimilarly,writing′DerivativesofElementaryCombinationsofFunctionsForexample,forf(x)=sin(x),wegetf0(x)=cos(x)Forexample,writing′ representsthederivativeofthefunctionevaluatedatpoint.BasicDifferentiationFormulas.Howcanwedothis?axasin(x)cos(x)sin(x)tan(x)sec2(x)cot(x) csc2(x)sec(x)tan(x)csc(x)cot(x)exaxHere,werepresentthederivativeofafunctionbyaprimesymbol