Techniques Of Differentiation

Slides:



Advertisements
Similar presentations
11.3:Derivatives of Products and Quotients
Advertisements

DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.
10.5 Basic Differentiation Properties. Instead of finding the limit of the different quotient to obtain the derivative of a function, we can use the rules.
Derivatives of polynomials Derivative of a constant function We have proved the power rule We can prove.
The Power Rule and other Rules for Differentiation Mr. Miehl
Rules for Differentiation. Taking the derivative by using the definition is a lot of work. Perhaps there is an easy way to find the derivative.
Chapter 3 Derivatives and Differentials 3.2 The rules for find derivative of a function.
Today in Calculus Go over homework Derivatives by limit definition Power rule and constant rules for derivatives Homework.
Differentiation Formulas
Chapter 4 Techniques of Differentiation Sections 4.1, 4.2, and 4.3.
3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.
2.3 The Product and Quotient Rules and Higher Order Derivatives
3.3 Rules for Differentiation. What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer.
Copyright © Cengage Learning. All rights reserved. 2 Derivatives.
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.
Slide 3- 1 Rule 1 Derivative of a Constant Function.
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.
3.3: Rules of Differentiation Objective: Students will be able to… Apply the Power Rule, Sum and Difference Rule, Quotient and Product Rule for differentiation.
AP Calculus BC September 9, 2015 Day 7 – The Chain Rule and Implicit Differentiation.
Section 2.5 – Implicit Differentiation. Explicit Equations The functions that we have differentiated and handled so far can be described by expressing.
Product & quotient rules & higher-order derivatives (2.3) October 17th, 2012.
3.3 Rules for Differentiation Quick Review In Exercises 1 – 6, write the expression as a power of x.
2.3 Differentiation Rules Colorado National Monument Larson, Hostetler, & Edwards.
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.
Techniques of Differentiation Notes 3.3. I. Positive Integer Powers, Multiples, Sums, and Differences A.) Th: If f(x) is a constant, PF:
Differentiability Arches National Park- Park Avenue.
3 DIFFERENTIATION RULES. We have:  Seen how to interpret derivatives as slopes and rates of change  Seen how to estimate derivatives of functions given.
Sec 3.3: Differentiation Rules Example: Constant function.
Powerpoint Templates Page 1 Powerpoint Templates Review Calculus.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Product and Quotient Rules for Differentiation.
2.5 Derivatives of Polynomials 1 The four-step process has been introduced to found derivatives. In the present and the next lecture, using this process,
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.
DO NOW: Write each expression as a sum of powers of x:
MTH 251 – Differential Calculus Chapter 3 – Differentiation Section 3.2 The Derivative as a Function Copyright © 2010 by Ron Wallace, all rights reserved.
Section 2.2a. Limits Involving Infinity We can say “the limit of f as x approaches infinity,” meaning the limit of f as x moves increasingly far to the.
Basic Rules of Derivatives Examples with Communicators Calculus.
3.3 Differentiation Rules Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.
2.3 Basic Differentiation Formulas
DIFFERENCE QUOTIENT, DERIVATIVE RULES, AND TANGENT LINES RIZZI – CALC BC.
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)
Announcements Topics: -sections 4.4 (continuity), 4.5 (definition of the derivative) and (differentiation rules) * Read these sections and study.
Basic derivation rules We will generally have to confront not only the functions presented above, but also combinations of these : multiples, sums, products,
§ 4.2 The Exponential Function e x.
Starter  .
Rules for Differentiation
AP Calculus BC September 12, 2016.
DIFFERENTIATION RULES.
2.3 Basic Differentiation Formulas
Aim: How do we determine if a function is differential at a point?
Techniques of Differentiation
2.2 Rules for Differentiation
3.2: Rules for Differentiation
Rules for Differentiation
Differentiation Rules
3.3 Techniques of Differentation
The Derivative: “Introduction to Techniques of Differentiation”
3.3 Differentiation Rules
Differentiation Rules
Derivatives of Polynomials and Exponential Functions
3.3 Differentiation Rules
Exponential and Logarithmic Derivatives
Rules for Differentiation
Tutorial 4 Techniques of Differentiation
Differentiation Techniques: The Power and Sum-Difference Rules
3.3 Differentiation Rules
Differentiation Techniques: The Power and Sum-Difference Rules
3.3 Differentiation Rules
L’Hôpital’s Rule Chapter 9.2.
2.5 Basic Differentiation Properties
Presentation transcript:

Techniques Of Differentiation • In the lectures so far, we obtained some derivatives directly by definition. • In this sections, we develop theorems which will give us short cuts for calculation derivatives of special functions • Derivatives of Constant Functions • Derivatives of Power functions • Derivative of a constant multiple of a function Etc!! • This result is also obvious geometrically since the function y = c is a horizontal line with slope 0. And we saw earlier that a line function has tangent line slope equal to its own slope which is 0.

Derivative of Sums and Differences of Functions Proof Similarly for difference left as exercise

Derivative of a product Same for general difference Derivative of a product

Derivative of a Quotient Prove yourself! Prove yourself!

Derivative of a Reciprocal Student can prove this using the quotient rule!!

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.