Rules for Differentiation

Slides:

Advertisements

Similar presentations

CHAPTER Continuity CHAPTER Derivatives of Polynomials and Exponential Functions.

Advertisements

3.9 Derivatives of Exponential and Logarithmic Functions.

3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.

3.3 Rules for Differentiation. What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer.

Chapter 3: Derivatives Section 3.3: Rules for Differentiation

Slide 3- 1 Rule 1 Derivative of a Constant Function.

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

3.3 Rules for Differentiation Quick Review In Exercises 1 – 6, write the expression as a power of x.

Differentiation Formulas

3.3 Rules for Differentiation Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer Powers of x Second and Higher.

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.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rules for Differentiation Section 3.3.

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.

Sec 3.3: Differentiation Rules Example: Constant function.

CHAPTER Continuity The Product and Quotient Rules Though the derivative of the sum of two functions is the the sum of their derivatives, an analogous.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Product and Quotient Rules for Differentiation.

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.

AP Calculus Chapter 3 Section 3

DO NOW: Write each expression as a sum of powers of x:

5.3 Definite Integrals and Antiderivatives. What you’ll learn about Properties of Definite Integrals Average Value of a Function Mean Value Theorem for.

Quick Review Find each sum: (-3) + (-3) + (-3) Answers:

Calculus I Ms. Plata Fortunately, several rules have been developed for finding derivatives without having to use the definition directly. Why?

Math 1411 Chapter 2: Differentiation 2.3 Product and Quotient Rules and Higher-Order Derivatives.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 1 Quick Review.

Basic derivation rules We will generally have to confront not only the functions presented above, but also combinations of these : multiples, sums, products,

Rules for Differentiation

Product and Quotient Rules and Higher-Order Derivatives

Chapter 5 The Definite Integral. Chapter 5 The Definite Integral.

Derivatives of Exponential and Logarithmic Functions

Definite Integrals and Antiderivatives

Implicit Differentiation

Estimating with Finite Sums

Objective: To Divide Integers

Multiplying and dividing integers

AP Calculus Honors Ms. Olifer

2.2 Rules for Differentiation

Chapter 3 Derivatives.

Rules for Differentiation

Rules for Differentiation

Sec 3.1: DERIVATIVES of Polynomial and Exponential

Derivatives of Exponential and Logarithmic Functions

Extreme Values of Functions

Connecting f′ and f″ with the graph of f

Chapter 8 Applications of Definite Integral Section 8.3 Volumes.

Chapter 4 More Derivatives Section 4.1 Chain Rule.

Chapter 8 Section 8.2 Applications of Definite Integral

Chapter 6 Applications of Derivatives Section 6.5 Trapezoidal Rule.

Unit 3 More Derivatives Chain Rule.

Chapter 5 Applications of Derivatives Section 5.6 Related Rates.

Chapter 5 Applications of Derivatives Section 5.6 Related Rates.

Definite Integrals and Antiderivatives

Implicit Differentiation

Implicit Differentiation

Linearization and Newton’s Method

Connecting f′ and f″ with the graph of f

Velocity and Other Rates of Change

Chapter 6 Applications of Derivatives Section 6.2 Definite Integrals.

Chapter 9 Section 9.2 L’Hôpital’s Rule

Linearization and Newton’s Method

Chapter 5 Applications of Derivatives Section 5.2 Mean Value Theorem.

Extreme Values of Functions

Derivatives of Exponential and Logarithmic Functions

Velocity and Other Rates of Change

Definite Integrals & Antiderivatives

Derivatives of Exponential and Logarithmic Functions

Chapter 4 More Derivatives Section 4.1 Chain Rule.

Implicit Differentiation

Fundamental Theorem of Calculus

Velocity and Other Rates of Change

Presentation transcript:

Rules for Differentiation Chapter 3 Derivatives Section 3.3 Rules for Differentiation

Quick Review

Quick Review

Quick Review

Quick Review Solutions

Quick Review Solutions

Quick Review Solutions

What you’ll learn about Power functions Sum and difference rules Product and quotient rules Negative integer powers of x Second and higher order derivatives … and why These rules help us find derivatives of functions analytically in a more efficient way.

Rule 1 Derivative of a Constant Function

Rule 2 Power Rule for Positive Integer Powers of x.

Rule 3 The Constant Multiple Rule

Rule 4 The Sum and Difference Rule

Example Positive Integer Powers, Multiples, Sums, and Differences

Example Positive Integer Powers, Multiples, Sums, and Differences

Rule 5 The Product Rule

Example Using the Product Rule

Rule 6 The Quotient Rule Rule 6 The Quotient Rule

Example Using the Quotient Rule

Rule 7 Power Rule for Negative Integer Powers of x

Example Negative Integer Powers of x

Second and Higher Order Derivatives

Second and Higher Order Derivatives

Quick Quiz Sections 3.1 – 3.3

Quick Quiz Sections 3.1 – 3.3

Quick Quiz Sections 3.1 – 3.3

Quick Quiz Sections 3.1 – 3.3

Quick Quiz Sections 3.1 – 3.3

Quick Quiz Sections 3.1 – 3.3