
Understanding the Derivative of x^N

Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Hard
Jennifer Brown
FREE Resource
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical concepts were covered in the previous parts of the series?
Statistics, probability, and calculus
Factorials, combinations, and the binomial theorem
Integration, differentiation, and limits
Algebra, geometry, and trigonometry
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the general formula for finding the derivative of a function f(x)?
f(x) = x^2 + 2x + 1
f'(x) = x^N - 1
f'(x) = lim (h -> 0) [f(x + h) - f(x)] / h
f(x) = x^N + N
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the function f(x + H) expressed when f(x) = x^N?
f(x + H) = x^N + H
f(x + H) = x^N * H
f(x + H) = x^N - H
f(x + H) = (x + H)^N
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which theorem is used to expand (x + H)^N?
Taylor Series
Binomial Theorem
Fundamental Theorem of Calculus
Pythagorean Theorem
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to the terms in the expression after dividing by H?
They become negative
They remain unchanged
They double in value
They all become zero
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the limit as H approaches zero in the expression?
All terms become zero
Only the last term remains
All terms become infinite
Only the first term remains
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final result of the derivative of x^N with respect to x?
N * x^(N-1)
N * x^N
N * x^(N+1)
x^N
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