Calculus Section 2.3 The Product and Quotient Rules and Higher-Order Derivatives.

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
AP Calculus Review
Section 3.5a. Evaluate the limits: Graphically Graphin What happens when you trace close to x = 0? Tabular Support Use TblStart = 0, Tbl = 0.01 What does.
Do Now Find the tangents to the curve at the points where
The Chain Rule Section 2.4.
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:
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 11e – Slide 1 of 55 § 4.2 The Exponential Function e x.
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 2.3: Product and Quotient Rule. Objective: Students will be able to use the product and quotient rule to take the derivative of differentiable.
The Product Rule The derivative of a product of functions is NOT the product of the derivatives. If f and g are both differentiable, then In other words,
Product and Quotient Rules and Higher – Order Derivatives
MATH 31 LESSONS Chapters 6 & 7: Trigonometry 9. Derivatives of Other Trig Functions.
1 The Product and Quotient Rules and Higher Order Derivatives Section 2.3.
Special Derivatives. Derivatives of the remaining trig functions can be determined the same way. 
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.
3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.
2.3 The 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.
Chapter 3: Derivatives Section 3.3: Rules for Differentiation
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.
Product & quotient rules & higher-order derivatives (2.3) October 17th, 2012.
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.
Differentiation Formulas
The Quotient Rule. Objective  To use the quotient rule for differentiation.  ES: Explicitly assessing information and drawing conclusions.
h Let f be a function such that lim f(2 + h) - f(2) = 5.
Ms. Battaglia AB/BC Calculus. The product of two differentiable functions f and g is itself differentiable. Moreover, the derivative of fg is the first.
4.2:Derivatives of Products and Quotients Objectives: Students will be able to… Use and apply the product and quotient rule for differentiation.
AP Calculus BC Monday, 21 September 2015 OBJECTIVES TSW find (1) derivatives using the product and quotient rules, and (2) higher-order derivatives. ASSIGNMENT.
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?
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.
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.
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.
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 –
AP Calculus Chapter 3 Section 3
3.6 Trigonometric Functions Wed Oct 21 Do Now Find the y’’ and y’’’ 1) 2)
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.
2-3: Product / Quotient Rules & Other Derivatives ©2002 Roy L. Gover Objectives: Learn and use the product & quotient rules. Derive.
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.
The Product and Quotient Rules and Higher-Order Derivatives Calculus 2.3.
Math 1411 Chapter 2: Differentiation 2.3 Product and Quotient Rules and Higher-Order Derivatives.
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.
HIGHER-ORDER DERIVATIVES Unit 3: Section 3 continued.
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.
Announcements Topics: -sections 4.4 (continuity), 4.5 (definition of the derivative) and (differentiation rules) * Read these sections and study.
Chapter 3 Derivatives.
Section 3.3 The Product and Quotient Rule
Section 2-3b The Product Rule
3.6 Trigonometric Functions Tues Sept 27
Techniques of Differentiation
Chapter 3 Derivatives.
Techniques Of Differentiation
Trigonometric functions
The Derivative: “Derivatives of Trigonometric Functions”
AP Calculus October 2, 2014 Mr. Agnew
PRODUCT AND QUOTIENT RULES AND HIGHER-ORDER DERIVATIVES
PRODUCT AND QUOTIENT RULES AND HIGHER-ORDER DERIVATIVES
Presentation transcript:

Calculus Section 2.3 The Product and Quotient Rules and Higher-Order Derivatives

The Product Rule The product of two differentiable functions is differentiable. The first times the derivative of the second plus the second times the derivative of the first.

The Quotient Rule The quotient of two differentiable functions is differentiable at all values of x such that g(x) doesn’t equal zero.

Speak Like a Pirate: Calculus Lodhi minus hidlo, Square the denominator, And you’re good to go! -Kwo Shunt Ruel-

Speak Like A Pirate Day

Proof of The Derivative of Tangent

Derivatives of Trig Functions

Proof of The Other Three Now, prove the other three trigonometric functions: Textbook p. 125 # 81