
Understanding Derivatives with Product and Chain Rules

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Aiden Montgomery
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main challenge in finding the derivative of the given function?
The function is already in its simplest form.
The function is a trigonometric function.
The function involves a product and a power.
The function is a simple polynomial.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which rule is necessary to apply when dealing with the product of two functions?
Power Rule
Quotient Rule
Product Rule
Sum Rule
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in applying the product rule to the given functions?
Apply the chain rule first.
Differentiate the entire function directly.
Simplify the function before differentiating.
Identify and differentiate each function separately.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of introducing the variable 'U' in the chain rule application?
To simplify the outer function.
To represent the entire function.
To isolate the inner function for differentiation.
To eliminate the need for the product rule.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the derivative of the inner function 'U' calculated?
By using the quotient rule.
By differentiating with respect to 'U' and multiplying by 'U' prime.
By integrating the function.
By applying the product rule.
Tags
CCSS.HSA.APR.A.1
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of multiplying 2X, 4, and 14X in the simplification process?
28X squared
112X squared
224X squared
56X squared
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the greatest common factor identified in the simplification process?
2 and three factors of 7X squared - 2
14X and one factor of 7X squared - 2
4 and two factors of 7X squared - 2
7X squared - 2
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