Implicit Differentiation

Slides:



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

Derivative Review Part 1 3.3,3.5,3.6,3.8,3.9. Find the derivative of the function p. 181 #1.
DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Implicit Differentiation Section 3.7.
Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.
3.6 Derivatives of Logarithmic Functions 1Section 3.6 Derivatives of Log Functions.
Chapter : Derivatives Section 3.7: Implicit Differentiation
3.7 Implicit Differentiation xf(x)f(x)g(x)g(x) f ‘ (x)g ‘ (x) 2821/3 33 33 4422 5.
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
MAT 125 – Applied Calculus 3.2 – The Product and Quotient Rules.
Implicit Differentiation 3.6. Implicit Differentiation So far, all the equations and functions we looked at were all stated explicitly in terms of one.
1 Implicit Differentiation. 2 Introduction Consider an equation involving both x and y: This equation implicitly defines a function in x It could be defined.
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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.6 Chain Rule.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Product and Quotient Rules for Differentiation.
Slide 3- 1 Quick Quiz Sections 3.4 – Implicit Differentiation.
Chapter 8 The Tangent Space. Contents: 8.1 The Tangent Space at a Point 8.2 The Differential of a Map 8.3 The Chain Rule 8.4 Bases for the Tangent Space.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.7 Implicit Differentiation.
The Chain Rule. The Chain Rule Case I z x y t t start with z z is a function of x and y x and y are functions of t Put the appropriate derivatives along.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 1 Quick Review.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 1.
MTH 251 – Differential Calculus Chapter 3 – Differentiation Section 3.7 Implicit Differentiation Copyright © 2010 by Ron Wallace, all rights reserved.
Chapter 3 Derivatives.
Rules for Differentiation
2.5 The Chain Rule If f and g are both differentiable and F is the composite function defined by F(x)=f(g(x)), then F is differentiable and F′ is given.
Chapter 14 Partial Derivatives.
Implicit Differentiation
4.2 Implicit Differentiation
Implicit Differentiation
Implicit Differentiation
Chapter 11 Additional Derivative Topics
Section 3.7 Implicit Functions
Implicit Differentiation
Chapter 3: Differentiation Topics
Chain Rules for Functions of Several Variables
Derivatives of Exponential and Logarithmic Functions
Quick Review.
MTH1170 Implicit Differentiation
Implicit Differentiation Implicit differentiation
Implicit Differentiation
Implicit Differentiation
Implicit Differentiation
Techniques of Differentiation
Chapter 3 Derivatives.
Rules for Differentiation
Rules for Differentiation
2.5 Implicit Differentiation
Implicit Differentiation
Derivatives of Exponential and Logarithmic Functions
Chapter 4 More Derivatives Section 4.1 Chain 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
Linearization and Newton’s Method
Rules for Differentiation
2.5 Implicit Differentiation
Section 3.7 Implicit Differentiation
Linearization and Newton’s Method
Derivatives of Exponential and Logarithmic Functions
Definite Integrals & Antiderivatives
2.5 The Chain Rule.
Derivatives of Exponential and Logarithmic Functions
Implicit Differentiation
Chapter 4 More Derivatives Section 4.1 Chain Rule.
Implicit Differentiation
Fundamental Theorem of Calculus
Chapter 4 More Derivatives Section 4.1 Chain Rule.
Presentation transcript:

Implicit Differentiation Chapter 4 More Derivatives Implicit Differentiation

Quick Review

Quick Review

Quick Review

Quick Review Solutions

Quick Review Solutions

Quick Review Solutions

What you’ll learn about Implicitly defined functions Using the Chain Rule to find derivatives of functions defined implicitly Tangent and normal lines to implicitly defined curves Finding higher order derivatives of implicitly defined functions Extending the Power Rule from integer powers to rational powers … and why Implicit differentiation allows us to find derivatives of functions that are not defined or written explicitly as a function of a single variable.

Implicitly Defined Functions

Example 1

Implicitly Defined Functions

Example Implicitly Defined Functions

Implicit Differentiation Process

Example Lenses, Tangents and Normal Lines

Example Lenses, Tangents and Normal Lines

Example Derivatives of a Higher Order

Quick Checkpoint: Chain Rule & Implicit Differentiation

Quick Quiz Sections 4.1 – 4.2

Quick Quiz Sections 4.1 – 4.2

Quick Quiz Sections 4.1 – 4.2

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

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