Calculus Product Rule Derivatives
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Product Rule in calculus?
Back
The Product Rule is a formula used to find the derivative of the product of two functions. If u(x) and v(x) are functions, then the derivative of their product is given by: (uv)' = u'v + uv'.
2.
FLASHCARD QUESTION
Front
If y = (x - 1)(x + 2), what is the first step to find dy/dx using the Product Rule?
Back
Identify the two functions: u = (x - 1) and v = (x + 2).
3.
FLASHCARD QUESTION
Front
What is the derivative of u = (x - 1)?
Back
The derivative u' = 1.
4.
FLASHCARD QUESTION
Front
What is the derivative of v = (x + 2)?
Back
The derivative v' = 1.
5.
FLASHCARD QUESTION
Front
Using the Product Rule, what is dy/dx for y = (x - 1)(x + 2)?
Back
dy/dx = (x - 1)'(x + 2) + (x - 1)(x + 2)' = 1(x + 2) + (x - 1)(1) = x + 2 + x - 1 = 2x + 1.
6.
FLASHCARD QUESTION
Front
What does the notation dy/dx represent?
Back
dy/dx represents the derivative of y with respect to x, indicating the rate of change of y as x changes.
7.
FLASHCARD QUESTION
Front
What is the significance of the Product Rule in calculus?
Back
The Product Rule is significant because it allows for the differentiation of products of functions, which is essential in many applications of calculus.
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