2.4 The Chain Rule.

Slides:

Advertisements

Similar presentations

Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve. 2.3 Derivatives of Trigonometric.

Advertisements

Product & Quotient Rules Higher Order Derivatives

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

1.4 – Differentiation Using Limits of Difference Quotients

The Power Rule  If we are given a power function:  Then, we can find its derivative using the following shortcut rule, called the POWER RULE:

The Chain Rule Section 2.4.

2.4 Chain Rule. Chain Rule If y=f(u) is a differentiable function of u and u=g(x) is a differentiable function of x then y=f(g(x)) is a differentiable.

Section 2.4 – The Chain Rule. Example 1 If and, find. COMPOSITION OF FUNCTIONS.

Section 2.4 – The Chain Rule

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

Warm Up: h(x) is a composite function of f(x) and g(x). Find f(x) and g(x)

1 The Product and Quotient Rules and Higher Order Derivatives Section 2.3.

How can one use the derivative to find the location of any horizontal tangent lines? How can one use the derivative to write an equation of a tangent line.

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.

Differentiating exponential functions.

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

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.

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.

Objectives: 1.Be able to find the derivative using the Constant Rule. 2.Be able to find the derivative using the Power Rule. 3.Be able to find the derivative.

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

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

Objectives: 1.Be able to find the derivative using the Constant Rule. 2.Be able to find the derivative using the Power Rule. 3.Be able to find the derivative.

3.3 Product and Quotient Rule Fri Sept 25 Do Now Evaluate each 1) 2) 3)

Examples A: Derivatives Involving Algebraic Functions.

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.

Calculus and Analytical Geometry Lecture # 8 MTH 104.

1 The Chain Rule Section After this lesson, you should be able to: Find the derivative of a composite function using the Chain Rule. Find the derivative.

Quotient Rule Finding the derivative of a function using the Quotient Rule Andrew Conway.

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.

Aim: How do we find the derivative by limit process? Do Now: Find the slope of the secant line in terms of x and h. y x (x, f(x)) (x + h, f(x + h)) h.

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.

The Chain Rule Composite Functions When a function is composed of an inner function and an outer function, it is called a “composite function” When a.

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

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

Product and Quotient Rule Find the derivative of the function using the Product Rule Find the derivative of the function using the Quotient Rule Find the.

More with Rules for Differentiation Warm-Up: Find the derivative of f(x) = 3x 2 – 4x 4 +1.

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

Derivative Shortcuts -Power Rule -Product Rule -Quotient Rule -Chain Rule.

After the test… No calculator 3. Given the function defined by for a) State whether the function is even or odd. Justify. b) Find f’(x) c) Write an equation.

Basic Rules of Derivatives Examples with Communicators Calculus.

2.3 Basic Differentiation Formulas

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

§ 4.2 The Exponential Function e x.

Chapter 3 Derivatives.

AP Calculus BC September 12, 2016.

Used for composite functions

3.1 Polynomial & Exponential Derivatives

2.3 Basic Differentiation Formulas

CHAPTER 4 DIFFERENTIATION.

Techniques of Differentiation

47 – Derivatives of Trigonometric Functions No Calculator

Techniques of Differentiation

Chapter 3 Derivatives.

2.4 The Chain Rule Use the Chain Rule to find derivative of a composite function. Use the General Power Rule to find derivative of a function. Simplify.

Exam2: Differentiation

The Chain Rule Section 4 Notes.

Basic Differentiation Rules

Exam2: Differentiation

§ 4.3 Differentiation of Exponential Functions.

COMPOSITION OF FUNCTIONS

The Chain Rule Section 3.4.

Tutorial 4 Techniques of Differentiation

3. Differentiation Rules

Chapter 3 Chain Rule.

The Chain Rule Section 2.4.

3. Differentiation Rules

2.5 Basic Differentiation Properties

Applied Calculus CH3 Part II Formative

Differentiation Rules for Products, Quotients,

Presentation transcript:

2.4 The Chain Rule

Decomposition of a Composite Function

Using Chain Rule

Applying the General Power Rule Find the derivative of:

Differentiating Functions Involving Radicals Find all points on the graph of f(x) for which f’(x)=0 and those for which f’(x) does not exist.

Differentiating Quotients with Constant Numerators Differentiate:

Simplifying by Factoring Out the Least Powers

Simplifying the Derivative of a Quotient

Simplifying the Derivative of a Power

Trigonometric Functions and the Chain Rule

Applying the Chain Rule to Trigonometric Functions

Parentheses and Trigonometric Functions

Parentheses and Trigonometric Functions

Repeated Application of the Chain Rule

Tangent Line of a Trigonometric Function Find an equation of the tangent line to the graph of f(x) at the point (π,1). Then determine all values of x in the interval (0,2π) at which the graph of f has a horizontal tangent.