2.1 Derivatives Great Sand Dunes National Monument, Colorado Vista High, AB Calculus. Book Larson, V9 2010Photo by Vickie Kelly, 2003.

Slides:

Advertisements

Similar presentations

3.1 Derivative of a Function

Advertisements

3.3 Differentiation Rules

3.1 Derivatives Great Sand Dunes National Monument, Colorado Photo by Vickie Kelly, 2003 Created by Greg Kelly, Hanford High School, Richland, Washington.

3.1 Derivatives Great Sand Dunes National Monument, Colorado Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

2.3 Rules for Differentiation Colorado National Monument Vista High, AB Calculus. Book Larson, V9 2010Photo by Vickie Kelly, 2003.

3.1 Derivatives. Derivative A derivative of a function is the instantaneous rate of change of the function at any point in its domain. We say this is.

2.5 Implicit Differentiation Niagara Falls, NY & Canada Photo by Vickie Kelly, 2003.

The Chain Rule Section 3.6c.

The Derivative 3.1. Calculus Derivative – instantaneous rate of change of one variable wrt another. Differentiation – process of finding the derivative.

DERIVATIVE OF A FUNCTION 1.5. DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,

The Derivative and the Tangent Line Problem

2.1 The derivative and the tangent line problem

2.2 The derivative as a function

3.1 Derivative of a Function

is called the derivative of at. We write: “The derivative of f with respect to x is …” There are many ways to write the derivative.

Warmup Find k such that the line is tangent to the graph of the function.

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

Derivatives of Powers and Polynomials Colorado National Monument Greg Kelly, Hanford High School, Richland, Washington Adapted by: Jon Bannon Siena College.

Rules for Differentiation Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

Derivatives. What is a derivative? Mathematically, it is the slope of the tangent line at a given pt. Scientifically, it is the instantaneous velocity.

3.3 Rules for Differentiation Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 The “Coke Ovens”,

3.1 Definition of the Derivative & Graphing the Derivative

11-2 Key to evens 2a) -5 2b) -3 2c) 0 4a) 0 4b) 1 4c) -2 6) -1/10 8) -5 10) 27 12) - 7/14 14) 1/8 16) 1/16 18) 0 20) 1/4 22) -1/6 24) 4 26) -1/4 28) 1.

3.3 Rules for Differentiation Colorado National Monument.

Introduction. Elements differential and integral calculations.

Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 AP Calculus AB/BC 3.3 Differentiation Rules,

3.2 Derivatives Great Sand Dunes National Monument, Colorado Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

3.1 Derivatives of a Function, p. 98 AP Calculus AB/BC.

Slide 3- 1 What you’ll learn about Definition of a Derivative Notation Relationship between the Graphs of f and f ' Graphing the Derivative from Data One-sided.

Derivatives Great Sand Dunes National Monument, Colorado Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

Apollonius was a Greek mathematician known as 'The Great Geometer'. His works had a very great influence on the development of mathematics and his famous.

Chapter 17.2 The Derivative. How do we use the derivative?? When graphing the derivative, you are graphing the slope of the original function.

Blue part is out of 50 Green part is out of 50  Total of 100 points possible.

The Second Derivative Greg Kelly, Hanford High School, Richland, Washington Adapted by: Jon Bannon Siena College 2008 Photo by Vickie Kelly, 2003 Arches.

2.1 The Derivative and the Tangent Line Problem (Part 1) Great Sand Dunes National Monument, Colorado Greg Kelly, Hanford High School, Richland, WashingtonPhoto.

2.1 Rates of Change and Tangent Lines Devil’s Tower, Wyoming Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1993.

3.1 Derivative of a Function Definition Alternate Definition One-sided derivatives Data Problem.

3.3 Differentiation Rules Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

2.2 Derivatives Great Sand Dunes National Monument, Colorado Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

2.3 The Product and Quotient Rules (Part 1)

2.7 and 2.8 Derivatives Great Sand Dunes National Monument, Colorado

Mean Value Theorem for Derivatives

3.3 Rules for Differentiation

Aim: How do we determine if a function is differential at a point?

Colorado National Monument

Differentiation Rules

Derivative of a Function

3.3 Differentiation Rules

Derivatives Great Sand Dunes National Monument, Colorado Greg Kelly

Derivatives Sec. 3.1.

3.1 Derivatives Part 2.

3.3 Differentiation Rules

Differentiation Rules

5.3 Inverse Function (part 2)

2.1 The Derivative & the Tangent Line Problem

2.1 The Derivative and the Tangent Line Problem

3.3 Differentiation Rules

Rules for Differentiation

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

Colorado National Monument

2.7 Derivatives Great Sand Dunes National Monument, Colorado

3.3 Rules for Differentiation

3.1 Derivatives of a Function

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

3.1 Derivatives Great Sand Dunes National Monument, Colorado

3.1 Derivatives Great Sand Dunes National Monument, Colorado

3.3 Differentiation Rules

3.3 Differentiation Rules

5.3 Inverse Function (part 2)

Presentation transcript:

2.1 Derivatives Great Sand Dunes National Monument, Colorado Vista High, AB Calculus. Book Larson, V9 2010Photo by Vickie Kelly, 2003

is called the derivative of at. We write: “The derivative of f with respect to x is …” There are many ways to write the derivative of

“f prime x”or “the derivative of f with respect to x” “y prime” “dee why dee ecks” or “the derivative of y with respect to x” “dee eff dee ecks” or “the derivative of f with respect to x” “dee dee ecks uv eff uv ecks”or “the derivative of f of x”

dx does not mean d times x ! dy does not mean d times y !

does not mean ! (except when it is convenient to think of it as division.) does not mean ! (except when it is convenient to think of it as division.)

(except when it is convenient to treat it that way.) does not mean times !

In the future, all will become clear.

The derivative is the slope of the original function. The derivative is defined at the end points of a function on a closed interval.

A function is differentiable if it has a derivative everywhere in its domain. It must be continuous and smooth. Functions on closed intervals must have one-sided derivatives defined at the end points. 