Unit 5 WU: Day 3 (Calculus)

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Mathematics
•
12th Grade
•
Hard
Standards-aligned
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1.
FLASHCARD QUESTION
Front
What is the quotient rule in calculus?
Back
The quotient rule states that if you have a function v = f/g, then the derivative v' is given by (vu' - uv')/v².
2.
FLASHCARD QUESTION
Front
How do you find the derivative of a function that is a quotient of two functions?
Back
To find the derivative of a function that is a quotient, apply the quotient rule: v' = (f'g - fg')/g².
3.
FLASHCARD QUESTION
Front
What is the derivative of y(x) = (4x² + 3)/(2x² - 5)?
Back
y' = -52x/(2x² - 5)².
4.
FLASHCARD QUESTION
Front
What is the derivative of g(x) = (3x - 2)/(x² + 2)?
Back
g' = (-3x² + 4x + 6)/(x² + 2)².
5.
FLASHCARD QUESTION
Front
Given f(2) = 3, g(2) = -3, f'(2) = 5, and g'(2) = 1, what is v'(2) if v = f/g?
Back
v'(2) = -2.
Tags
CCSS.HSF-BF.A.1B
6.
FLASHCARD QUESTION
Front
What is the general formula for the derivative of a quotient of two functions?
Back
If v = f/g, then v' = (f'g - fg')/g².
7.
FLASHCARD QUESTION
Front
What is the significance of the derivative in calculus?
Back
The derivative represents the rate of change of a function with respect to its variable.
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