What is the Product Rule for derivatives?
Derivatives on Product & Quotient Rule

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Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
If u(x) and v(x) are functions, then the derivative of their product is given by: (u*v)' = u'v + uv'.
2.
FLASHCARD QUESTION
Front
What is the Quotient Rule for derivatives?
Back
If u(x) and v(x) are functions, then the derivative of their quotient is given by: (u/v)' = (u'v - uv')/v^2.
3.
FLASHCARD QUESTION
Front
Find the derivative of g(x) = (3x - 2)/(x^2 + 2).
Back
g'(x) = (-3x^2 + 4x + 6)/(x^2 + 2)^2.
4.
FLASHCARD QUESTION
Front
Find the derivative of the function f(x) = x^3 + x^2 + 12.
Back
f'(x) = 3x^2 + 2x.
5.
FLASHCARD QUESTION
Front
What does it mean for the slope of the tangent line to be zero?
Back
The slope of the tangent line is zero at points where the function has a local maximum or minimum.
6.
FLASHCARD QUESTION
Front
How do you find the equation of the tangent line at a point?
Back
Use the point-slope form: y - f(a) = f'(a)(x - a), where a is the point of tangency.
7.
FLASHCARD QUESTION
Front
Find the tangent line to the curve y = \frac{12}{x^2} at x = 2.
Back
The tangent line is y = -3x + 9.
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