
Understanding Derivatives and Chain Rule

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

Ethan Morris
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in applying the chain rule to a function?
Find the derivative of the outer function.
Find the derivative of the inner function.
Multiply the function by its derivative.
Add the derivatives of all terms.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you handle negative exponents when finding derivatives?
Convert them to fractions first.
Apply the power rule as usual.
Treat them as positive exponents.
Ignore them.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of x^3 + 2x^2 - x^-2?
3x^2 + 4x - 2x^-3
3x^2 + 4x + 2x^-3
3x^2 + 4x + x^-3
3x^2 - 4x + 2x^-3
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of simplifying the derived expression?
To eliminate negative exponents.
To convert it to a polynomial.
To find the slope at any point.
To make it easier to integrate.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In a complex chain rule problem, what is the strategy for finding the derivative?
Start with the outermost function.
Use integration by parts.
Differentiate all terms simultaneously.
Start with the innermost function.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of 3x^-2 + 5x^3 - 7x to the fifth power?
15x^2 - 7
15x^2 + 7x
15x^2 + 7
15x^2 - 7x
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you handle nested functions in the chain rule?
Differentiate the outer function only.
Differentiate from the outermost to the innermost.
Differentiate each function separately.
Differentiate from the innermost to the outermost.
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