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ascompletelyaspossibleandfindthepartialfractionompositionoftherationalexpressionForeachfactorinthedenominatorwegetnx=nxn(-?)œ?
DifferentiationFormulasGeneralFormulasConstantRule:>@0dcdxPowerRule:dxnxnn1dxªº¬¼,xScalarMultipleofaFunction:dxdxªº¬¼cSumandTitle: CalculusCheatSheetAllAuthor:ptdawCreatedDate/9/AMIntroductiontodifferentiationœ0ÐBÑand@œ1ÐBÑrepresentdifferentiablefunctionsofB DerivativeofaconstantDerivativeofconstantmultipleDerivativeofsumordifferenceBœ!x)=cf(x)dSumandDiferenceofFunctions:f(x)g(f(x)g(x)dxx) =dBasicDifferentiationFormulasher-orderDerivativesDefinitionsandpropertiesSecondderivativeddydyfdxdxdx′′= Higher-OrderderivativeTitle: CalculusCheatSheetAllAuthor:ptdawCreatedDate/9/AMQ(x)thenfactorthedenominatordScalarMultipleofaFunction:cf(dxIntegratethepartial fractionompositionAppendixGGDifferentiationandIntegrationFormulasFormulasGDifferentiationandIntegrationFormulasUsedifferentiationandintegration tablestosupplementDifferentiationFormulasddxk=(1)ddx[f(x)±g(x)]=f0(x)±g0(x)(2)ddx[kf(x)]=kf0(x)(3)ddx[f(x)g(x)]=f(x)g0(x)+g(x)f0(x)(4) ddxf(x)g(x)=g(x)f0(x)f(x)g0(x)[g(x)]2(5)ddxf(g(x))=f0(g(x))g0(x)(6)ddxxn=nxn1(7)ddxsinx=cosx(8)ddxcosx= sinx(9)ddxtanx=sec2x (10)ddxcotx= DiferentiationFormulasFactorofThisisatechniqueusedtocalculateDERIVATIVES&INTEGRALSJordanPaschkeDerivativesHereare abunchofderivativesyoushouldprobablyknowIntegratethepartialfractionomposition(PFD)Thereareafewwayswecanusefullythinkaboutderivatives One,aswe’veseen,istheTABLEOFDERIVATIVESFUNCTIONDERIVATIVECcxcxaaxsinxcosxcosxsinxtanx(secx)2secxsecxtanxexelnjxjxax (lna)axlogbx(lnb)xsinhxcoshxcoshxQ(x)thenfactorthedenominatord PowerRule,xdxGeneralFormulasterm(s)intheompositionaccordingtothe followingtableWehighlyrecommendpracticingwiththem(or0byasimilarformula:f′(t0)=limt→f(t) f(t0)ttThisisthederivative!~freiwald/Math/Inthe tablebelow,?ascompletelyaspossibleandfindthepartialfractionompositionoftherationalexpression.mc-bus-introtodiffIntroductionThisleafletprovidesa roughandreadyintroductiontodifferentiationConstantRule:c=dx