December 6, 2012 AIM : How do we find the derivative of quotients? Do Now: Find the derivatives HW2.3b Pg. 126 - 128 #7 – 11 odd, 15, 65, 81, 95, 105 –

Slides:



Advertisements
Similar presentations
Complex Functions These derivatives involve embedded composite, product, and quotient rules. The functions f or g must be derived using another rule.
Advertisements

U2 L5 Quotient Rule QUOTIENT RULE
Chapter 3: Functions and Graphs 3.5: Operations on Functions
Do Now Find the tangents to the curve at the points where
Area Between Two Curves 7.1. Area Formula If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the.
Section 2.3: Product and Quotient Rule. Objective: Students will be able to use the product and quotient rule to take the derivative of differentiable.
 Simplify the following. Section Sum: 2. Difference: 3. Product: 4. Quotient: 5. Composition:
Product and Quotient Rules and Higher – Order 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.
3.2 The Product and Quotient Rules DIFFERENTIATION RULES In this section, we will learn about: Formulas that enable us to differentiate new functions formed.
2.4 The Chain Rule Remember the composition of two functions? The chain rule is used when you have the composition of two functions.
Aim: Product/Quotient & Higher Order Derivatives Course: Calculus Do Now: Aim: To memorize more stuff about differentiation: Product/quotient rules and.
Derivatives of Products and Quotients Lesson 4.2.
2.4 The Chain Rule. We now have a pretty good list of “shortcuts” to find derivatives of simple functions. Of course, many of the functions that we will.
HIGHER ORDER DERIVATIVES Product & Quotient Rule.
Chapter 4 Additional Derivative Topics
3.3 Product and Quotient Rule Fri Sept 25 Do Now Evaluate each 1) 2) 3)
Product and Quotient Rules. Product Rule Many people are tempted to say that the derivative of the product is equal to the product of the derivatives.
Section 3.3 The Product and Quotient Rule. Consider the function –What is its derivative? –What if we rewrite it as a product –Now what is the derivative?
AP CALCULUS 1009 : Product and Quotient Rules. PRODUCT RULE FOR DERIVATIVES Product Rule: (In Words) ________________________________________________.
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.
State Standard – 15.0b Students use the fundamental theorem of calculus to interpret integrals as antidervivatives. – 14.0 Students apply the definition.
D ERIVATIVES Review- 6 Differentiation Rules. For a function f(x) the instantaneous rate of change along the function is given by: Which is called the.
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.
Lesson 2-8: Operations of Functions
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.
Warm Up Write an equation of the tangent line to the graph of y = 2sinx at the point where x = π/3.
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???
DO NOW: Write each expression as a sum of powers of x:
Review of 1.4 (Graphing) Compare the graph with.
Calculus I Ms. Plata Fortunately, several rules have been developed for finding derivatives without having to use the definition directly. Why?
The Product and Quotient Rules for Differentiation.
Calculus Section 2.3 The Product and Quotient Rules and Higher-Order Derivatives.
3.3 Product Rule Tues Oct 27 Do Now Evaluate each 1) 2)
The Product Rule. Ideally, we can operate on expressions in factored form. Expanding expressions just to work with them seems time consuming. f(x) = (3x.
3.1 The Product and Quotient Rules & 3.2 The Chain Rule and the General Power Rule.
AP CALCULUS 1008 : Product and Quotient Rules. PRODUCT RULE FOR DERIVATIVES Product Rule: (In Words) ________________________________________________.
4.2:DERIVATIVES OF PRODUCTS AND QUOTIENTS Objectives: To use and apply the product and quotient rule for differentiation.
Product and Quotient Rules
3.5 Operations on Functions
Section 3.3 The Product and Quotient Rule
Find the derivative Find the second derivative
Section 2-3b The Product Rule
Calculus Section 3.6 Use the Chain Rule to differentiate functions
3.1 Polynomial & Exponential Derivatives
The Quotient Rule Used to find derivatives when functions are expressed as ratios (division) Bottom times the derivative of the top minus the top times.
CHAPTER 4 DIFFERENTIATION.
Techniques of Differentiation
MATH 1310 Test 3 Review 10 Multiple Choice (worth 60 points)
Derivatives of Products and Quotients
Product and Quotient Rules
Chain Rule AP Calculus.
2.4 The Chain Rule.
Derivatives of Logarithmic Functions
3.11: Derivatives of Inverse Functions
The Chain Rule Section 4 Notes.
MATH 1310 Test 3 Review 10 Multiple Choice (worth 60 points)
PRODUCT AND QUOTIENT RULES AND HIGHER-ORDER DERIVATIVES
31 – Power, Product, Quotient Rule No Calculator
6-1: Operations on Functions (+ – x ÷)
MATH 1310 Test 3 Review 10 Multiple Choice (worth 60 points)
Composition of Functions
2.1 Functions.
The Product & Quotient Rules
Chapter 3 Chain Rule.
PRODUCT AND QUOTIENT RULES AND HIGHER-ORDER DERIVATIVES
Chapter 3 Additional Derivative Topics
Presentation transcript:

December 6, 2012 AIM : How do we find the derivative of quotients? Do Now: Find the derivatives HW2.3b Pg #7 – 11 odd, 15, 65, 81, 95, 105 – 108

How can we find the derivative of

The Quotient Rule How can we find the derivative of Or, we can use the Quotient Rule: If f and g are differentiable functions, then f/g is a differentiable for all x such that g(x) ≠ 0, and “The bottom times the derivative of the top minus the top times the derivative of the bottom over the bottom squared”

Example Use the product rule to find the derivative of Step 1: Define f(x) and g(x) Step 2: Find f’(x) and g’(x) Step 3: Plug into formula and simplify

Practice 1.Find 2.Find

Practice!