【2017年整理】多元函数求导经典例题

多元函数习题课;一 学习要求;(3) 理解偏导数和全微分的概念,会求全微分,了解全微分存在的必要和充分条件,了解全微分形式不变性;;偏导数的应用;二、主要内容;全微分的应用;1.区域;(3)n维空间;2.多元函数概念;3.多元函数的极限;说明：;5.多元函数的连续性;6.闭区域上连续函数的性质;7.偏导数概念;;;８.高阶偏导数;９.偏导数在经济上的应用:交叉弹性;即;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;10.全微分概念;多元函数连续、可导、可微的关系;11.全微分的应用;12.复合函数求导法则;;13.全微分形式不变性;隐函数的求导公式;;15.多元函数的极值;多元函数取得极值的条件;;;条件极值：对自变量有附加条件的极值．;三、典型例题;解;解;解 (1);解;解：;解:;思考与练习;解法2 令;解法3 令;2 函数的连续性、可导、可微等;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;矛盾;练习：教材P221 T13;多元函数连续、可导、可微的关系;解:;解:;解:;例9;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;强调:;解;例11;例12. 设;例13;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;5 二重积分对称问题;测 验 题 ;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.;测验题答案;Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.