【步步高】（江苏专用）2017版高考数学一轮复习第三章导数及其应用3.1导数的概念及运算文INCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\基础知识自主学习.tif"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\基础知识自主学习.tif"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\基础知识自主学习.tif"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\基础知识自主学习.tif"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\知识梳理.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\知识梳理.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\知识梳理.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\知识梳理.TIF"\*MERGEFORMATINET1．导数与导函数的概念(1)设函数y＝f(x)在区间(a，b)上有定义，x0∈(a，b)，若Δx无限趋近于0时，比值＝无限趋近于一个常数A，则称f(x)在x＝x0处可导，并称该常数A为函数f(x)在x＝x0处的导数(derivative)，记作f′(x0)．(2)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．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)．3．基本初等函数的导数公式基本初等函数导函数f(x)＝C(C为常数)f′(x)＝0f(x)＝xα(α为常数)f′(x)＝αxα－1f(x)＝sinxf′(x)＝cos_xf(x)＝cosxf′(x)＝－sin_xf(x)＝exf′(x)＝exf(x)＝ax(a>0，a≠1)f′(x)＝axln_af(x)＝lnxf′(x)＝f(x)＝logax(a>0，a≠1)f′(x)＝4.导数的运算法则若f′(x)，g′(x)存在，则有(1)[f(x)±g(x)]′＝f′(x)±g′(x)；(2)[f(x)·g(x)]′＝f′(x)g(x)＋f(x)g′(x)；(3)[]′＝(g(x)≠0)．【思考辨析】1判断下面结论是否正确(请在括号中打“√”或“×”)(1)f′(x0)与(f(x0))′表示的意义相同．(×)(2)求f′(x0)时，可先求f(x0)再求f′(x0)．(×)(3)曲线的切线不一定与曲线只有一个公共点．(√)(4)与曲线只有一个公共点的直线一定是曲线的切线．(×)(5)函数f(x)＝sin(－x)的导数是f′(x)＝cosx．(×)INCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\考点自测2.tif"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\考点自测2.tif"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\考点自测2.tif"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\考点自测2.tif"\*MERGEFORMATINET1．(教材改编)f′(x)是函数f(x)＝x3＋2x＋1的导函数，则f′(－1)的值为________．答案3解析 f(x)＝x3＋2x＋1，∴f′(x)＝x2＋2.∴f′(－1)＝3.2．如图所示为函数y＝f(x)，y＝g(x)的导函数的图象，那么y＝f(x)，y＝g(x)的图象可能是________．INCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-1.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-1.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-1.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-1.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-2.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-2.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-2.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-2.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵丽君2016\\一轮2016\\数学\\苏教（文）\\3-3.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\赵...
