
Understanding the Product Rule in Differentiation

Interactive Video
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Mathematics
•
9th - 12th Grade
•
Hard

Lucas Foster
FREE Resource
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5 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the product rule of differentiation state?
The derivative of a quotient is the quotient of the derivatives.
The derivative of a product is the first function times the derivative of the second plus the second function times the derivative of the first.
The derivative of a product is the product of the derivatives.
The derivative of a sum is the sum of the derivatives.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example f(x) = 3x^4 * cos(x), what is the derivative of U, where U = 3x^4?
12x^3
3x^3
4x^3
12x^4
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of V, where V = cos(x), in the example?
-sin(x)
cos(x)
sin(x)
-cos(x)
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
After applying the product rule to f(x) = 3x^4 * cos(x), what is the expression for f'(x) before factoring?
3x^4 * sin(x) - cos(x) * 12x^3
3x^4 * cos(x) + sin(x) * 12x^3
3x^4 * cos(x) - sin(x) * 12x^3
3x^4 * sin(x) + cos(x) * 12x^3
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the factored form of the derivative f'(x) for the function f(x) = 3x^4 * cos(x)?
3x^3(sin(x) + x cos(x))
3x^3(cos(x) - x sin(x))
3x^3(sin(x) - x cos(x))
3x^3(cos(x) + x sin(x))
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