[2014创新设计高中数学苏教版第三章第1讲导数的概念与运算.ppt

第1讲　导数的概念与运算 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 考点梳理 1．函数y＝f(x)在x＝x0处的导数 A Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (2)几何意义：函数f(x)在点x0处的导数f′(x0)的几何意义是过曲线y＝f(x)上点___________的切线的斜率． 若f(x)对于区间(a，b)内任一点都可导，则f(x)在各点的导数也随着自变量x的变化而变化，因而也是自变量x的函数．该函数称为f(x)的导函数，记作f′(x)． 2．函数f(x)的导函数 (x0，f(x0)) 3．基本初等函数的导数公式 原函数 导函数 f(x)＝C f′(x)＝____ f(x)＝xα(α为常数) f′(x)＝_______ f(x)＝sin x f′(x)＝________ 0 αxα－1 cos_x Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. f(x)＝cos x f′(x)＝_________ f(x)＝ax(a0，a≠1) f′(x)＝_______ f(x)＝ex f′(x)＝_______ f(x)＝logax(a＞0，a≠1) f′(x)＝________ f(x)＝ln x f′(x)＝______　　 －sin x axln a ex Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (1)[f(x)±g(x)]′＝____________； (2)[f(x)·g(x)]′＝_________________； 若y＝f(u)，u＝ax＋b，则yx′＝________，即yx′＝yu′·a. f′(x)±g′(x) f′(x)g(x)＋f(x)g′(x) 4.导数的运算法则 5．复合函数的导数 yu′·ux′ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 　一个命题规律 本讲知识是高考中的常考内容，尤其是导数的几何意义及导数的四则运算，更是高考考查的重点．以填空题的形式出现，有时也出现在解答题的第一问中．导数的运算及复合函数的导数一般不单独考查，在考查导数应用的同时考查导数的运算． 【助学·微博】 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 曲线y＝f(x)“在点P(x0，y0)处的切线”与“过点P(x0，y0)的切线”的区别与联系 (1)曲线y＝f(x)在点P(x0，y0)处的切线是指P为切点，切线斜率为k＝f′(x0)的切线，是唯一的一条切线． (2)曲线y＝f(x)过点P(x0，y0)的切线，是指切线经过P点．点P可以是切点，也可以不是切点，而且这样的直线可能有多条． Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解析　f(1)＝0，f′(x)＝3x2－4x，f′(1)＝－1，所以切线方程为y＝－(x－1)，即x＋y－1＝0. 答案　x＋y－1＝0 考点自测 1．(2012·济南模拟)曲线f(x)＝x2(x－2)＋1在点(1，f(1))处的切线方程为________． Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.