Understanding Derivatives and the Chain Rule
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Aiden Montgomery
FREE Resource
Standards-aligned
Read more
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main goal when analyzing the function f(x) in this tutorial?
To graph f(x)
To solve f(x) for x
To find the derivative f'(x)
To find the integral of f(x)
Tags
CCSS.HSF-BF.A.1C
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which function is identified as the outer function in the composite function f(x)?
Exponential function
Sine function
Inverse tangent function
Cosine function
Tags
CCSS.HSF-BF.A.1C
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the inner function u in the composite function f(x)?
exponential(2x)
sine(2x)
cosine(2x)
tangent(2x)
Tags
CCSS.HSF-BF.A.1C
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What rule is used to find the derivative of the inner function u?
Chain rule
Quotient rule
Product rule
Power rule
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the inner function u, which is sine(2x)?
sine(2x)
2 sine(2x)
2 cosine(2x)
cosine(2x)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the expression for f'(x) after applying the derivative formula?
2 sine(2x) / (1 + cosine^2(2x))
2 cosine(2x) / (1 + sine^2(2x))
4 cosine(2x) / (1 + sine^2(2x))
4 sine(2x) / (1 + sine^2(2x))
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplified form of the numerator in the expression for f'(x)?
2 sine(2x)
4 cosine(2x)
4 sine(2x)
2 cosine(2x)
Tags
CCSS.HSF.TF.C.9
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