Why is it important to use parentheses when writing functions like f(x) = sin^4 x?

Understanding Derivatives of Composite Functions

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

Aiden Montgomery
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
To confuse students
To ensure the function is evaluated correctly
To make the function look more complex
To make the function easier to read
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the derivative of f(x) = (sin x)^4?
Use the double angle identity
Apply the product rule
Differentiate directly
Identify the inner function
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the function f(x) = (sin x)^4, what is the derivative of the inner function?
4x^3
cos x
sin x
x^4
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of f(x) = (sin x)^4 in terms of x?
4 sin^3 x cos x
4x^3 cos x
sin^4 x
cos x sin^3 x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does the derivative of f(x) = sin(x^4) differ from that of f(x) = (sin x)^4?
It does not require the chain rule
It uses the product rule
It is the same
It has a different inner function
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the inner function in f(x) = sin(x^4)?
cos x
4x^3
x^4
sin x
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the inner function in f(x) = sin(x^4)?
x^4
sin x
cos x
4x^3
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