托马斯微积分课件2.5 The Chain Rule and Parametric Equations.ppt

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1、Chapter2Derivatives2.3DerivativesofProducts,Quotients,andNegativePowers2.1TheDerivativeasaFunction2.2TheDerivativeasaRateofChange2.4DerivativesofTrigonometricFunctions2.5TheChainRuleandParametricEquations2.6ImplicitDifferentiation2.7RelatedRates2.5TheChainRuleandParametricEquations2

2、.5.1DerivativeofaCompositeFunction2.5.2“Outside-Inside”Rule2.5.3SlopesofParametrizedCurves2.5.1DerivativeofaCompositeFunction在点x可导,定理3.在点可导复合函数且在点x可导,在点x可导,定理3.在点可导复合函数且在点x可导,GeneralizationofTheorem3.FindthederivativeofthefunctionExample1.FindthederivativeofthefunctionSolution.Solut

3、ion.思考:若存在,如何求的导数?这两个记号含义不同Example2.FindthederivativeofthefunctionExample3.SupposedfindthederivativeofthefunctionSolution.isderivative,tryto_______________________________________________Second-Orderderivative?2.5.3SlopesofParametrizedCurves若参数方程可确定一个y与x之间的函数可导,且则时,有关系,Byparametricf

4、ormula,wehaveExample.Supposed,andLet’strytofindSolution.ExercisesP19518,23,25,31,40,43.P19651(d,e,h),61.