Presentation is loading. Please wait.

Presentation is loading. Please wait.

Www.apcalculusbc.com. 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.

Published byCandice Butler Modified over 8 years ago

Similar presentations

Presentation on theme: "Www.apcalculusbc.com. 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."— Presentation transcript:

1 www.apcalculusbc.com

2 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 www.apcalculusbc.com

3 “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” www.apcalculusbc.com

4 dx does not mean d times x ! dy does not mean d times y ! www.apcalculusbc.com

5 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.)

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

7 In the future, all will become clear.

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

9

10 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.  www.apcalculusbc.com

Download ppt "Www.apcalculusbc.com. 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."

Similar presentations

3.1 Derivative of a Function

3.1 Derivative of a Function
3.7 Implicit Differentiation

3.7 Implicit Differentiation
3.3 Differentiation Rules

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 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.

3.1 Derivatives Great Sand Dunes National Monument, Colorado Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.
2.1 Derivatives Great Sand Dunes National Monument, Colorado Vista High, AB Calculus. Book Larson, V9 2010Photo by Vickie Kelly, 2003.

2.1 Derivatives Great Sand Dunes National Monument, Colorado 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.

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.
Warm Up Sketch the graph of y = ln x What is the domain and range?

Warm Up Sketch the graph of y = ln x What is the domain and range?
The Chain Rule Section 3.6c.

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.

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:,,,

DERIVATIVE OF A FUNCTION 1.5. DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,
The Derivative and the Tangent Line Problem

The Derivative and the Tangent Line Problem
The Derivative and the Tangent Line Problem. Local Linearity.

The Derivative and the Tangent Line Problem. Local Linearity.
2.1 The derivative and the tangent line problem

2.1 The derivative and the tangent line problem
Sec. 4.5: Integration by Substitution. T HEOREM 4.12 Antidifferentiation of a Composite Function Let g be a function whose range is an interval I, and.

Sec. 4.5: Integration by Substitution. T HEOREM 4.12 Antidifferentiation of a Composite Function Let g be a function whose range is an interval I, and.
2.2 The derivative as a function

2.2 The derivative as a function
Economics 214 Lecture 17 Derivatives and differentials.

Economics 214 Lecture 17 Derivatives and differentials.
Www.apcalculusbc.com. We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:

We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:
If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.
3.1 Derivative of a Function

3.1 Derivative of a Function

Similar presentations

Ads by Google