Product & Quotient Rule 3.3. The Product Rule The first times the derivative of the second plus the second times the derivative of the first When two.

Slides:



Advertisements
Similar presentations
Variables and Expressions
Advertisements

Product & Quotient Rules Higher Order Derivatives
Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate…
The Quotient Rule Brought To You By Tutorial Services The Math Center.
3.3 Rules for Differentiation
11.3:Derivatives of Products and Quotients
4n + 6 A number increased by six times four A number plus six
Are You Smarter Than a 5 th Grader? 1,000,000 5th Grade Topic 1 5th Grade Topic 2 4th Grade Topic 3 4th Grade Topic 4 3rd Grade Topic 5 3rd Grade Topic.
Do Now Find the tangents to the curve at the points where
(2.8) Factoring Special Products OBJECTIVE: To Factor Perfect Square Trinomials and Differences of Squares.
SQUARE ROOT METHOD. Simplify Radicals A. Single Ex.
The Product and Quotient Rules
Business Calculus Derivatives. 1.5 – 1.7 Derivative Rules  Linear Rule:   Constant Rule:   Power Rule:   Coefficient Rule:   Sum/Difference Rule:
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.
Multiplying Positive & Negative Numbers. -6 x –4 = =
Product and Quotient Rules and Higher – Order Derivatives
Finding an Inverse Function with a Table. Inverse Notation Original function Inverse function “Inverse of f(x)”
Addition, Subtraction, Multiplication, and Division of Integers
3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.
3.3 Rules for Differentiation. What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer.
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.
Chapter 3: Derivatives Section 3.3: Rules for Differentiation
In this section, we will investigate how to take the derivative of the product or quotient of two functions.
3.3 Rules for Differentiation AKA “Shortcuts”. Review from places derivatives do not exist: ▫Corner ▫Cusp ▫Vertical tangent (where derivative is.
Chapter 1-1: Variables and Expressions. Example 1 Write Algebraic Expressions Write an algebraic expression for each verbal expression. ◦a number k minus.
Jarrod Asuncion Period 1 Brose. Simple Derivatives Sample 1 ◊^n = something to the “something” power n ∙ ◊^n-1 ∙ d◊ = multiply something by ‘n’ and the.
Section 6.1 Polynomial Derivatives, Product Rule, Quotient Rule.
Conditions : Perfect cube #’s ( 1, 8, 27, 64, 125, … ) Perfect cube exponents ( 3, 6, 9, 12,15, … ) Separated by a plus OR minus sign Factoring – Sum and.
Derivatives of Products and Quotients Lesson 4.2.
Differentiation Formulas
The Quotient Rule. Objective  To use the quotient rule for differentiation.  ES: Explicitly assessing information and drawing conclusions.
The Quotient Rule. The following are examples of quotients: (a) (b) (c) (d) (c) can be divided out to form a simple function as there is a single polynomial.
h Let f be a function such that lim f(2 + h) - f(2) = 5.
4.2:Derivatives of Products and Quotients Objectives: Students will be able to… Use and apply the product and quotient rule for differentiation.
1.6 – Differentiation Techniques The Product and Quotient Rules.
Katie Bisciotti Alyssa Mayer Andrew Stacy
Chapter 4 Additional Derivative Topics
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.
Product and Quotient Rule By: Jenna Neil Lori Hissick And Evan Zimmerman Period 4.
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?
By: Susana Cardona & Demetri Cheatham © Cardona & Cheatham 2011.
 1. Square the first term.  2. Double the product of the two terms.  3. Square the last term.  Ex:  (2x – 1) 2  4x 2 - 4x + 1 Perfect square trinomial.
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.
Quotient Rule Finding the derivative of a function using the Quotient Rule Andrew Conway.
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 –
2-3: Product / Quotient Rules & Other Derivatives ©2002 Roy L. Gover Objectives: Learn and use the product & quotient rules. Derive.
Multiplying Monomials. Monomial – Any number, or variable, or product /quotient of numbers and variables. Ex: 6x 6x - x 2 y 2 - y 2 z 3 ½xy In an expression,
INTEGER RULES. Adding Integers Adding IntegersRule # 1: Same Signs When adding integers with same signs, you add the numbers and write the common sign.
Calculus I Ms. Plata Fortunately, several rules have been developed for finding derivatives without having to use the definition directly. Why?
Difference of Two Perfect Squares
The Product and Quotient Rules and Higher-Order Derivatives Calculus 2.3.
Calculus Section 2.3 The Product and Quotient Rules and Higher-Order Derivatives.
4.2:DERIVATIVES OF PRODUCTS AND QUOTIENTS Objectives: To use and apply the product and quotient rule for differentiation.
CFU Perform operations with numbers in scientific notation (multiply, divide, powers). SPI Multiply, divide, and square numbers expressed.
The Product and Quotient rules
Chain Rule.
Section 3.3 The Product and Quotient Rule
Fun facts about derivatives.
وكيفية عمل التقدير النجمي
2.2 Rules for Differentiation
Calculating the Derivative
The Derivative as a Function
Product and Quotient Rules and Higher Order Derivatives
AP Calculus October 2, 2014 Mr. Agnew
26. Section 4.7 L’Hopital’s Rule
Product and Quotient Rules and Higher Order Derivatives
Subtracting Real Numbers
PRODUCT AND QUOTIENT RULES AND HIGHER-ORDER DERIVATIVES
Dividing Radical Expressions
Differentiation Rules for Products, Quotients,
Presentation transcript:

Product & Quotient Rule 3.3

The Product Rule The first times the derivative of the second plus the second times the derivative of the first When two things are multiplied and you know how to find the derivative of each separately you can use the product rule

The Product Rule The first times the derivative of the second plus the second times the derivative of the first 1 st 2 nd

If we multiply out the original problem we can avoid the product rule but in later sections we will have problems where we can’t avoid using the product rule

Quotient Rule or Which is read lo d-hi minus hi d-lo over lo squared

Quotient Rule

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

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