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Quotient rule (AASL/HL)

Författare/skapare:Cliff Packman

Keywords

Quotient rule商の法則분수 규칙商规则
Differential calculus微分計算法미분 계산법微分学
Derivative微分미분导数
Functions quotient関数の商함수의 몫函数的商
Rates of change変化率변화율变化率
Numerator and denominator functions分子と分母の関数분자 및 분모 함수分子和分母函数
Factual Inquiry QuestionsConceptual Inquiry QuestionsDebatable Inquiry Questions
1. What is the quotient rule in differential calculus?1. Why is the quotient rule necessary for differentiating quotients of functions, and how does it differ from simply dividing their individual derivatives?1. Is the quotient rule more prone to errors in application than the product rule due to its complexity?
2. How is the quotient rule applied to find the derivative of the quotient of two functions?2. How does the quotient rule illustrate the relationship between the rates of change of the numerator and denominator functions?2. Could the principles of the quotient rule be simplified or improved to make calculus more accessible to beginners?
3. How might the role of the quotient rule in teaching calculus evolve with the increasing use of technology in education?

Inquiry questions

Factual Inquiry Questions What is the quotient rule in differential calculus? How is the quotient rule applied to find the derivative of the quotient of two functions? Conceptual Inquiry Questions Why is the quotient rule necessary for differentiating quotients of functions, and how does it differ from simply dividing their individual derivatives? How does the quotient rule illustrate the relationship between the rates of change of the numerator and denominator functions? Debatable Inquiry Questions Is the quotient rule more prone to errors in application than the product rule due to its complexity? Could the principles of the quotient rule be simplified or improved to make calculus more accessible to beginners? How might the role of the quotient rule in teaching calculus evolve with the increasing use of technology in education?
Mini-Investigation: The Quotient Quest Welcome, brave Calculus Explorer! Today, we set sail on a mathematical voyage to uncover the mysteries of the Quotient Rule. Are you ready to unravel the enigma of dividing functions?

Chapter 1: Discovery of the Quotient Realm In the land of Numeratoria and Denominatoria, two functions u(x) and v(x) live in harmony. Your first discovery is their quotient, y = (x + 3) / x. 1. Imagine u(x) and v(x) are two different territories. How do they come together to form the landscape of y? 2. Without using the Quotient Rule, can you find an alternative path to travel from u(x)/v(x) to dy/dx?

Chapter 2: The Quotient Rule Riddle A legendary scroll reveals the Quotient Rule, a powerful formula: dy/dx = (v du/dx - u dv/dx) / v^2. It's time to decipher this riddle! 1. Apply the Quotient Rule to u(x) and v(x). Document each magical transformation step by step. 2. Compare your journey using the Quotient Rule to the alternative path you found earlier. Which was more perilous and which was more straightforward?

Chapter 3: The Duel of Derivatives A challenge is issued! You must use both the Quotient Rule and the alternative method to find the derivative of a new territory, . 1. Calculate using both methods. Which one brings you to the solution faster? 2. Is there treasure to be found in understanding both methods? What insights do they offer about the changing landscape of y?

Question 1: If and , what is the derivative of ?

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Chapter 4: Realms of Application Beyond the theoretical world lies a vast expanse of practical applications, where the Quotient Rule helps navigate complex terrains. 1. In the realm of the real world, where might the Quotient Rule be essential for understanding rates of change? 2. Can you find a situation where the alternative method might provide deeper understanding, despite potentially being more complex?

Part 2 - Checking your understanding

See how you do with these questions. Attempt these questions. Watch the video to see the quotient rule in action

Question 2: Given and , what is the derivative of ?

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Question 3: If and , what is the derivative of ?

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Question 4: Consider and . What is the derivative of the quotient ?

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Question 5: If and , what is the derivative of ?

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Part 3 - Exam style questions

Question 1-9 - Practice questions Question 10-25 - Section A short response exam-style Question 26-27 - Section B long response exam-style Question 5, 12, 14, 18 specifically require use of quotient rule

[MAA 5.2] DERIVATIVES - BASIC RULES

[MAA 5.2] DERIVATIVES - BASIC RULES.pdf

[MAA 5.2] DERIVATIVES - BASIC RULES.pdf

[MAA 5.2] DERIVATIVES - BASIC RULES_solutions

[MAA 5.2] DERIVATIVES - BASIC RULES_solutions.pdf

[MAA 5.2] DERIVATIVES - BASIC RULES_solutions.pdf

Lesson plan - Exploring the Quotient Rule in Differential Calculus

Exploring the Quotient Rule in Differential Calculus.pdf

Exploring the Quotient Rule in Differential Calculus.pdf

Quotient rule -- Intuition pump (thought experiments and analogies)

Quotient rule.pdf

Quotient rule.pdf

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