Mr. Jonathan Anderson MAT – 1710 Calculus & Analytic Geometry I SUNY JCC Jamestown, NY.

Slides:

Advertisements

Similar presentations

Section 3.5a. Evaluate the limits: Graphically Graphin What happens when you trace close to x = 0? Tabular Support Use TblStart = 0, Tbl = 0.01 What does.

Advertisements

The Derivative. Definition Example (1) Find the derivative of f(x) = 4 at any point x.

Partial Derivatives and the Gradient. Definition of Partial Derivative.

Assigned work: pg 74#5cd,6ad,7b,8-11,14,15,19,20 Slope of a tangent to any x value for the curve f(x) is: This is know as the “Derivative by First Principles”

Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.

The Derivative. Definition Example (1) Find the derivative of f(x) = 4 at any point x.

Derivatives of polynomials Derivative of a constant function We have proved the power rule We can prove.

Calculus Section 2.2 Basic Differentiation Rules and Rates of Change.

AP Calculus Chapter 2, Section 2 Basic Differentiation Rules and Rates of Change

The Power Rule and other Rules for Differentiation Mr. Miehl

SECTION 3.1 The Derivative and the Tangent Line Problem.

Calculus Warm-Up Find the derivative by the limit process, then find the equation of the line tangent to the graph at x=2.

The Derivative Definition, Interpretations, and Rules.

Today in Calculus Go over homework Derivatives by limit definition Power rule and constant rules for derivatives Homework.

Tangents and Differentiation

Techniques of Differentiation. I. Positive Integer Powers, Multiples, Sums, and Differences A.) Th: If f(x) is a constant, B.) Th: The Power Rule: If.

1.6 – Tangent Lines and Slopes Slope of Secant Line Slope of Tangent Line Equation of Tangent Line Equation of Normal Line Slope of Tangent =

The Derivative. Definition Example (1) Find the derivative of f(x) = 4 at any point x.

3.3 Rules for Differentiation What you’ll learn about Positive integer powers, multiples, sums, and differences Products and Quotients Negative Integer.

Techniques of Differentiation. I. Positive Integer Powers, Multiples, Sums, and Differences A.) Th: If f(x) is a constant, B.) Th: The Power Rule: If.

In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.

GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative.

AP Calculus Chapter 2, Section 1 THE DERIVATIVE AND THE TANGENT LINE PROBLEM 2013 – 2014 UPDATED

Powerpoint Templates Page 1 Powerpoint Templates Review Calculus.

Basic Differentiation Rules Rates of Change. The Constant Rule The derivative of a constant function is 0. Why?

SAT Prep. Basic Differentiation Rules and Rates of Change Find the derivative of a function using the Constant Rule Find the derivative of a function.

Basic Differentiation Rules The CONSTANT Rule: The derivative of a constant function is 0.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Differentiation Techniques: The Power and Sum-Difference Rules OBJECTIVES.

Calculus and Analytical Geometry Lecture # 8 MTH 104.

Sec. 3.3: Rules of Differentiation. The following rules allow you to find derivatives without the direct use of the limit definition. The Constant Rule.

Derivatives of Trigonometric Functions. 2 Derivative Definitions We can now use the limit of the difference quotient and the sum/difference formulas.

Calculus and Analytical Geometry

MAT 1221 Survey of Calculus Section 2.2 Some Rules for Differentiation

Today in Calculus Derivatives Graphing Go over test Homework.

2.1 The Derivative and the Tangent Line Problem.

Calculus Chapter 2 SECTION 2: THE DERIVATIVE AND THE TANGENT LINE PROBLEM 1.

Business Calculus Derivative Definition. 1.4 The Derivative The mathematical name of the formula is the derivative of f with respect to x. This is the.

Warm Ups. AP Calculus 3.1 Tangent Line Problem Objective: Use the definition to find the slope of a tangent line.

Basic Rules of Derivatives Examples with Communicators Calculus.

2.3 Basic Differentiation Formulas

AP Calculus 3.2 Basic Differentiation Rules Objective: Know and apply the basic rules of differentiation Constant Rule Power Rule Sum and Difference Rule.

Unit 2 Lesson #1 Derivatives 1 Interpretations of the Derivative 1. As the slope of a tangent line to a curve. 2. As a rate of change. The (instantaneous)

§ 4.2 The Exponential Function e x.

AP Calculus BC September 12, 2016.

2.1 Tangent Line Problem.

3.1 Polynomial & Exponential Derivatives

2.3 Basic Differentiation Formulas

The Derivative and the Tangent Line Problem (2.1)

The Tangent Line Problem

The Derivative and the Tangent Line Problems

Differentiation Rules (Constant, Power, Sum, Difference)

BASIC DIFFERENTIATION RULES AND RATES OF CHANGE

Derivatives by Definition

Pre-AP Pre-Calculus Chapter 5, Section 3

Differentiation Rules (Part 2)

Exam2: Differentiation

Derivatives of Polynomials and Exponential Functions

(This is the slope of our tangent line…)

2.1 The Derivative & the Tangent Line Problem

2.2 Basic Differentiation Rules and Rates of Change (Part 1)

Differentiation Rules and Rates of Change

The Tangent Line Problem

3.1 Derivatives.

2.2 Basic Differentiation Rules and Rates of Change (Part 1)

BASIC DIFFERENTIATION RULES AND RATES OF CHANGE

The Constant Rule m = 0 The derivative of a constant function is 0.

The Derivative and the Tangent Line Problem (2.1)

More with Rules for Differentiation

2.5 Basic Differentiation Properties

Presentation transcript:

Mr. Jonathan Anderson MAT – 1710 Calculus & Analytic Geometry I SUNY JCC Jamestown, NY

Vocab and Notation  The process of finding the derivative of a function is called differentiation.  To differentiate is to find the derivative.  4 different notations:

Continuity  Differentiability implies continuity.  Continuity does not imply differentiability (sharp point).  A function is differentiable at a point (x = c) iff a single tangent line to the curve can be drawn at that point.

Limit Definition

Example

Constant Rule  The derivative of a constant is zero.  Example:

Power Rule

Sum / Difference  The derivative of a sum/difference is the sum/difference of the derivatives.

Sine and Cosine

The Exponential Function

Application to Slope  If you evaluate the first derivative at x=c, that will be the slope of f(x) at x=c.  Therefore, the first derivative of a given function is the function that is collection of points representing the slopes of the given function.

Example

Homework  Pg. 136 # 3-23 [5], EOO, 56, 59-61