说明1导数概念.pdf

Chapter 3 Derivatives and Differentials 1. The Concepts of the Derivative 2. The Rules for Finding Derivatives 3. Higher-order Derivatives and Differentials of Functions 4. Differential Skill 3.1 The Concepts of the Derivative 1. Tangent Lines and Instantaneous Rates of Change 2. The Definition of Derivatives 3. Examples for Finding Derivations 4. Examples for Finding Derivations Geometric Interpretation of the Derivative 3.1. 5The Relationship between the Continuity and the Differentiability of Functions Words Derivative 导数 Derivable 可导的 Derivability 可导性 One-sided derivative 单侧导数 Left derivative 左导数 Right derivative 右导数 Tangent 切线 Secant 割线 Instantaneous rate of change 瞬时变化率 New words 切线方程 tangent equation 角速度 angular velocity 二阶函数 second derivative 三阶导数 third derivative 高阶导数 nth derivative Leibniz formula 可微的 differentiable 函数的微分 differential of function 自变量的微分differential of t variable 微商 differential quotient 水平 horizontal 对数求导法 log- derivative 垂直 vertical 参数方程 parametric equation 3.1.1Tangent Lines and Instantaneous Rates of Change See Figure y y = f (x) The average rate of change of y with respect to x over the interval with P Q endpoints x0 and x0 +Dx is T x Dy = f (x 0 +Dx) -f (x 0 ) O x 0 x0 +Dx Dx Dx This is the slope of the secant joining the points P (x0 , y 0 ) and Q(x0 +Dx , y 0 +Dy ) of the graph f . The slope of th