[2016年高三数学理创新设计资料包3-1.ppt

基础诊断 考点突破 课堂总结 第1讲 导数的概念及运算 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1．导数与导函数的概念 知 识 梳 理 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (2)如果函数y＝f(x)在开区间(a，b)内的每一点处都有导数，其导数值在(a，b)内构成一个新函数，这个函数称为函数y＝f(x)在开区间内的导函数．记作f′(x)或y′. 2．导数的几何意义 函数y＝f(x)在点x0处的导数的几何意义，就是曲线y＝f(x)在点P(x0，f(x0))处的切线的斜率k，即k＝______． f′(x0) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3．基本初等函数的导数公式 基本初等函数 f(x)＝c(c为常数) f(x)＝xα(α∈Q*) f(x)＝sin x f(x)＝cos x f(x)＝ex f(x)＝ax(a＞0，a≠1) f(x)＝ln x f(x)＝logax (a＞0，a≠1) 导函数 f′(x)＝___ f′(x)＝________ f′(x)＝______ f′(x)＝________ f′(x)＝____ f′(x)＝________ f′(x)＝____ f′(x)＝______ 0 αxα－1 cos x －sin x ex axln a Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 4. 导数的运算法则 若f′(x)，g′(x)存在，则有 (1)[f(x)±g(x)]′＝_______________； (2)[f(x)·g(x)]′＝____________________； 5．复合函数的导数 复合函数y＝f(g(x))的导数和函数y＝f(u)，u＝g(x)的导数间的关系为yx′＝________，即y对x的导数等于______的导数与_____的导数的乘积． f′(x)±g′(x) f′(x)g(x)＋f(x)g′(x) yu′·ux′ y对u u对x Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1．判断正误(在括号内打“√”或“×”)　 精彩PPT展示 (1)曲线的切线不一定与曲线只有一个公共点． ( ) (2)与曲线只有一个公共点的直线一定是曲线的切线． ( ) (3)已知曲线y＝x3，则过点P(1，1)的切线有两条． ( ) (4)物体的运动方程是s＝－4t2＋16t，在某一时刻的速度为0，则相应时刻t＝2. ( ) (5)[f(ax＋b)]′＝f′(ax＋b)． ( ) 诊 断 自 测 √ × √ √ × Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2．(2014·新课标全国Ⅱ卷)设曲线y＝ax－ln(x＋1)在点(0，0)处的切线方程为y＝2x，则a＝ (　　) A．0 B．1 C．2 D．3 答案　D Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3．(2015·保定调研)已知曲线y＝ln x的切线过原点，则此切线的斜率为