What is the main mathematical concept used to find the derivatives of composite functions?

Understanding Derivatives of Composite Functions

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

Sophia Harris
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Power Rule
Chain Rule
Quotient Rule
Product Rule
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of Big F(x) = F(x^3), what is identified as the inner function?
x
F(x^3)
x^3
F(x)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the derivative of Big F(x) expressed using the chain rule?
3x^2 * F'(x^3)
F'(x^3) * x^2
3 * F(x^3)
F(x^3) * 3x
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of Big F'(a) given a^2 = 12 and F'(a^3) = 4?
48
144
72
36
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of Big G(x) = (F(x))^3, what is identified as the outer function?
F(x)
x^3
(F(x))^3
x
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which rule is used to differentiate a function raised to a power in the context of the chain rule?
Product Rule
Quotient Rule
Power Rule
Sum Rule
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the derivative of Big G(x) expressed using the chain rule?
3 * (F(x))^2 * F'(x)
3 * F(x) * x
F(x) * F'(x)
F'(x) * 3
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