Chapter 3 Derivatives.

Slides:

Advertisements

Similar presentations

The Natural Logarithmic Function

Advertisements

DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.

© 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

© 2010 Pearson Education, Inc. All rights reserved.

Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.

Calculus Chapter 5 Day 1 1. The Natural Logarithmic Function and Differentiation The Natural Logarithmic Function- The number e- The Derivative of the.

Section 6.1: Euler’s Method. Local Linearity and Differential Equations Slope at (2,0): Tangent line at (2,0): Not a good approximation. Consider smaller.

3.6 Derivatives of Logarithmic Functions 1Section 3.6 Derivatives of Log Functions.

The Natural Logarithmic Function

1 6.5 Derivatives of Inverse Trigonometric Functions Approach: to differentiate an inverse trigonometric function, we reduce the expression to trigonometric.

3.5 – Derivative of Trigonometric Functions

Special Derivatives. Derivatives of the remaining trig functions can be determined the same way. 

7.3* The Natural Exponential Function INVERSE FUNCTIONS In this section, we will learn about: The natural exponential function and its properties.

4.1 Implicit Differentiation Definition. We will say that a given equation in x and y defines the function f implicitly if the graph of y = f(x)

(MTH 250) Lecture 11 Calculus. Previous Lecture’s Summary Summary of differentiation rules: Recall Chain rules Implicit differentiation Derivatives of.

Question If f is differentiable, find the limit Sol.

The chain rule (2.4) October 23rd, I. the chain rule Thm. 2.10: The Chain Rule: If y = f(u) is a differentiable function of u and u = g(x) is a.

Chapter 4 Techniques of Differentiation Sections 4.1, 4.2, and 4.3.

In this section, we will investigate a new technique for finding derivatives of curves that are not necessarily functions.

Chapter3: Differentiation DERIVATIVES OF TRIGONOMETRIC FUNCTIONS: Chain Rule: Implicit diff. Derivative Product Rule Derivative Quotient RuleDerivative.

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 3 Integration.

{ Chapter 4 Practice AP Calculus. Differentiate:

CHAPTER Continuity Implicit Differentiation.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.6 Chain Rule.

3.7 – Implicit Differentiation An Implicit function is one where the variable “y” can not be easily solved for in terms of only “x”. Examples:

CHAPTER 4 DIFFERENTIATION NHAA/IMK/UNIMAP. INTRODUCTION Differentiation – Process of finding the derivative of a function. Notation NHAA/IMK/UNIMAP.

Calculus and Analytical Geometry

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.

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

6.3 Antidifferentiation by Parts Quick Review.

7 INVERSE FUNCTIONS. 7.6 Inverse Trigonometric Functions In this section, we will learn about: Inverse trigonometric functions and their derivatives.

Logarithmic, Exponential, and Other Transcendental Functions

Chapter Three Differentiation. Copyright © Houghton Mifflin Company. All rights reserved. 3 | 2 Secant Line.

Section 6.2* The Natural Logarithmic Function. THE NATURAL LOGARITHMIC FUNCTION.

SECTION 5-1 The Derivative of the Natural Logarithm.

Calculus Review. Chapter 1 What is a function Linear Functions Exponential Functions Power Functions Inverse Functions Logs, ln’s and e’s Trig functions.

Linear Approximations. In this section we’re going to take a look at an application not of derivatives but of the tangent line to a function. Of course,

Inverse Trigonometric Functions: Differentiation & Integration (5. 6/5

Chapter 3 Derivatives Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

AP Calculus BC September 12, 2016.

Chapter 3 Differentiation

(8.2) - The Derivative of the Natural Logarithmic Function

Chain Rules for Functions of Several Variables

Used for composite functions

MTH1170 Implicit Differentiation

CHAPTER 4 DIFFERENTIATION.

Sec 3.5: IMPLICIT DIFFERENTIATION

47 – Derivatives of Trigonometric Functions No Calculator

Chapter 1 Functions.

Chapter 1 Functions.

Chapter 3 Derivatives.

Warm Up Six Chapter 5.5 Derivatives of base not e 11/20/2018

Calculating the Derivative

2.4 The Chain Rule.

Derivatives of Logarithmic Functions

Implicit Differentiation

Chapter 3 Integration Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Exam2: Differentiation

Implicit Differentiation

Derivatives of Inverse Functions

Chapter 3 Derivatives.

Exam2: Differentiation

Implicit Differentiation

Implicit Differentiation

Differentiate the function: {image} .

Sec 3.3: Derivatives Of Trigonometric Functions

Chapter 3 Derivatives.

Implicit Differentiation

Antidifferentiation by Parts

Presentation transcript:

Chapter 3 Derivatives

Tangent Lines and the Derivative at a Point Section 3.1 Tangent Lines and the Derivative at a Point

The Derivative as a Function 3.2 The Derivative as a Function

Differentiation Rules Section 3.3 Differentiation Rules

The Derivative as a Rate of Change Section 3.4 The Derivative as a Rate of Change

Derivatives of Trigonometric Functions Section 3.5 Derivatives of Trigonometric Functions

Section 3.6 The Chain Rule

Implicit Differentiation Section 3.7 Implicit Differentiation

Derivatives of Inverse Functions and Logarithms Section 3.8 Derivatives of Inverse Functions and Logarithms

Inverse Trigonometric Functions Section 3.9 Inverse Trigonometric Functions

Section 3.10 Related Rates

Linearization and Differentials Section 3.11 Linearization and Differentials