Monday, February 15, 2016MAT 145. Function typeDerivative Rule Constant for constant c Power for any real number n Product of constant and functions for.

Slides:

Advertisements

Similar presentations

2.4 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.

Advertisements

Monday, February 25, 2013MAT 145. Monday, February 25, 2013MAT 145.

The Derivative. Definition Example (1) Find the derivative of f(x) = 4 at any point x.

Rules for Differentiating Univariate Functions Given a univariate function that is both continuous and smooth throughout, it is possible to determine its.

CHAPTER Continuity CHAPTER Derivatives of Polynomials and Exponential Functions.

Friday, February 10, 2012MAT 121. Friday, February 10, 2012MAT 121.

Derivatives of Logarithmic Functions

In this section, we will learn about: Differentiating composite functions using the Chain Rule. DIFFERENTIATION RULES 3.4 The Chain Rule.

11.4 The Chain Rule.

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.

2.4 The Chain Rule Remember the composition of two functions? The chain rule is used when you have the composition of two functions.

Section 3.4 The Chain Rule. One of THE MOST POWERFUL Rules of Differentiation The chain rule allows you to take derivatives of compositions of functions.

Math 1304 Calculus I 3.4 – The Chain Rule. Ways of Stating The Chain Rule Statements of chain rule: If F = fog is a composite, defined by F(x) = f(g(x))

4009 Fundamental Theorem of Calculus (Part 2) BC CALCULUS.

MAT 213 Brief Calculus Section 3.4 The Chain Rule.

3.4 - The Chain Rule. The Chain Rule: Defined If f and g are both differentiable and F = f ◦ g is the composite function defined by F(x) = f(g(x)), then.

Calculus Section 2.4 The Chain Rule. Used for finding the derivative of composite functions Think dimensional analysis Ex. Change 17hours to seconds.

Thursday, February 9, 2012MAT 121. Thursday, February 9, 2012MAT 121.

Section 3.4 The Chain Rule. Consider the function –We can “decompose” this function into two functions we know how to take the derivative of –For example.

In this section, we will investigate how to take the derivative of a function that is the composition of multiple functions.

Lesson 4-2 Operations on Functions. We can do some basic operations on functions.

Sec 3.3: Differentiation Rules Example: Constant function.

The Product Rule for Differentiation. If you had to differentiate f(x) = (3x + 2)(x – 1), how would you start?

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.

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.

Chapter 4 Additional Derivative Topics Section 4 The Chain Rule.

Ch. 4 – More Derivatives 4.1 – Chain Rule. Ex: Find the derivative of h(x) = sin(2x 2 ). –This is not a product rule problem because it has one function.

Further Differentiation and Integration

Wednesday, Sept 30, 2015MAT 145. Wednesday, Sept 30, 2015MAT 145.

Monday, Sept 28, 2015MAT 145. Monday, Sept 28, 2015MAT 145.

Chain Rule 3.5. Consider: These can all be thought of as composite functions F(g(x)) Derivatives of Composite functions are found using the chain rule.

Chain Rule – Differentiating Composite Functions.

In this section, we will learn about: Differentiating composite functions using the Chain Rule. DERIVATIVES 3.5 The Chain Rule.

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

2.4: THE CHAIN RULE. Review: Think About it!!  What is a derivative???

Wednesday, February 8, 2012MAT 121. Wednesday, February 8, 2012MAT 121.

4.9 Antiderivatives Tues Dec 1 Do Now If f ’(x) = x^2, find f(x)

3.1 The Product and Quotient Rules & 3.2 The Chain Rule and the General Power Rule.

2-1 The Derivative and the Tangent Line Problem 2-2 Basic Differentiation Rules and Rates of Change 2-3 Product/Quotient Rule and Higher-Order Derivatives.

Wednesday, February 17, 2016MAT 145. Wednesday, February 17, 2016MAT 145 THE CHAIN RULE WORDS BY: JOHN A. CARTER TUNE: "CLEMENTINE" Here's a function.

The Chain Rule Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2002 online.math.uh.edu/HoustonACT/Greg_Kelly.../Calc03_6.ppt.

Friday, February 12, 2016MAT 145. Friday, February 12, 2016MAT 145.

Calculus I (MAT 145) Dr. Day Friday Feb 5, 2016

Chapter 4 Additional Derivative Topics Section 4 The Chain Rule.

Learning Objectives for Section 11.4 The Chain Rule

11.4 The Chain Rule.

Differentiation Product Rule By Mr Porter.

DIFFERENTIATION RULES

Calculus I (MAT 145) Dr. Day Monday Oct 9, 2017

Calculus Section 3.6 Use the Chain Rule to differentiate functions

Calculus I (MAT 145) Dr. Day Friday September 29, 2017

CHAPTER 4 DIFFERENTIATION.

Derivative of an Exponential

Copyright © Cengage Learning. All rights reserved.

Chain Rule AP Calculus.

2.4 The Chain Rule.

Implicit Differentiation

Perform Function Operations and Composition

Unit 3 More Derivatives Chain Rule.

The Chain Rule Find the composition of two functions.

Used for composite functions (a function within a function)…

6-1: Operations on Functions (+ – x ÷)

3.5 Chain Rule.

Calculus I (MAT 145) Dr. Day Monday February 18, 2019

3.6 – The Chain Rule.

Chapter 3 Chain Rule.

Chapter 3 Additional Derivative Topics

Differentiation and the Derivative

The Chain Rule.

Presentation transcript:

Monday, February 15, 2016MAT 145

Function typeDerivative Rule Constant for constant c Power for any real number n Product of constant and functions for constant c & function f(x) Sum or difference of functions for functions f(x) and g(x) Natural exponential function Exponential Functions for constant a Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145 THE CHAIN RULE WORDS BY: JOHN A. CARTER TUNE: "CLEMENTINE" Here's a function in a function And your job here is to find The derivative of the whole thing With respect to x inside. Call the outside f of u And call the inside u of x. Differentiate to find df/du And multiply by du/dx. Use the chain rule. Use the chain rule when e'er you find The derivative of a function compositionally defined.

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016 MAT 145

Monday, February 15, 2016MAT 145

Monday, February 15, 2016MAT 145