Understanding the Derivative of x^N

Understanding the Derivative of x^N

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

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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