The Product and Quotient Rules

Slides:



Advertisements
Similar presentations
U2 L5 Quotient Rule QUOTIENT RULE
Advertisements

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 1 of 55 § 4.2 The Exponential Function e 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.
Mrs. Rivas International Studies Charter School.Objectives: slopes and equations 1.Find slopes and equations of tangent lines. derivative of a function.
Implicit Differentiation
2.3 The Product and Quotient Rules and Higher Order Derivatives
MAT 125 – Applied Calculus 3.2 – The Product and Quotient Rules.
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.
In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
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.
AP CALCULUS 1009 : Product and Quotient Rules. PRODUCT RULE FOR DERIVATIVES Product Rule: (In Words) ________________________________________________.
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.
Implicit Differentiation Objective: To find derivatives of functions that we cannot solve for y.
Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2001 London Bridge, Lake Havasu City, Arizona 2.3 Product and Quotient Rules.
Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve.
Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.
Chapter 3 Limits and the Derivative
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.
DO NOW: Write each expression as a sum of powers of x:
Warm Up. Equations of Tangent Lines September 10 th, 2015.
Today in Calculus Derivatives Graphing Go over test Homework.
Calculus Chapter 2 SECTION 2: THE DERIVATIVE AND THE TANGENT LINE PROBLEM 1.
Derivative Notation and Velocity. Notation for the Derivative.
HIGHER-ORDER DERIVATIVES Unit 3: Section 3 continued.
AP CALCULUS 1008 : Product and Quotient Rules. PRODUCT RULE FOR DERIVATIVES Product Rule: (In Words) ________________________________________________.
3.2 (Day 2) Difference Quotient & Graphs of Functions.
§ 4.2 The Exponential Function e x.
2.3 The Product and Quotient Rules (Part 1)
Starter  .
Product and Quotient Rules
3-3 rules for differentiation
Implicit Differentiation
2-4 Rates of change & tangent lines
Section 11.3A Introduction to Derivatives
Implicit Differentiation
Find the equation of the tangent line for y = x2 + 6 at x = 3
2.1A Tangent Lines & Derivatives
3.1 Polynomial & Exponential Derivatives
3.3 Rules for Differentiation
Graphs and the Derivative
Implicit Differentiation
Techniques of Differentiation
3.2: Rules for Differentiation
2.4 The Chain Rule.
Derivatives of Logarithmic Functions
Question Suppose exists, find the limit: (1) (2) Sol. (1) (2)
The Derivative as a Function
Techniques Of Differentiation
The Chain Rule Section 4 Notes.
Derivatives of Polynomials and Exponential Functions
(This is the slope of our tangent line…)
Increasing & Decreasing Functions First Derivative Test
Limits at Infinity and Limits of Sequences
Graphs and the Derivative
Find the derivative Find the derivative at the following point.
10.2 Parametric Tangents & Areas
2.1B Derivative Graphs & Differentiability
7. Section 8.1 Length of a Curve
The Chain Rule Section 3.4.
The Chain Rule Section 3.6b.
Section 2.2 Day 2 Basic Differentiation Rules & Rates of Change
Copyright © Cengage Learning. All rights reserved.
The Chain Rule Section 3.4.
The Chain Rule Section 2.4.
Copyright © Cengage Learning. All rights reserved.
Chapter 3 Additional Derivative Topics
Presentation transcript:

The Product and Quotient Rules Section 3.2

Example 1, product rule (a) If f (x) = xex, find f (x). (b) Find the nth derivative, f (n)(x). Solution: (a) By the Product Rule

Example 1 – Solution f (x) = (x + 3)ex f (4)(x) = (x + 4)ex To generalize, f (n)(x) = (x + n)ex

Example 2, product rule

Example 3, quotient rule

Example 4, Tangent Line Find the tangent line to the curve at the point (1, ½ e) Horizontal at (1, ½ e)

3.2 The Product and Quotient Rules Summarize Notes Read section 3.2 Homework Pg.189 #3-34 (odd),41-43