3. Which of the following is the quotient rule for derivatives?

h'(x)=((g(x)f'(x) - f(x)g'(x)) / (g(x))2

h'(x)=((g(x)f'(x) + f(x)g'(x)) / (g(x))2

h'(x)=((g'(x)f'(x) - f(x)g(x)) / (g(x))

h'(x)=((g'(x)f'(x) + f(x)g(x)) / (g(x))

Chapter 12 : Limits And Derivatives

Reviewed by Editorial Team

The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.

Learn about Our Editorial Process

| By Esra

Esra

Community Contributor

Quizzes Created: 1 | Total Attempts: 151

| Attempts: 153

Quiz Flashcard Lesson

Questions

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

1/10 Questions

1. Which of the following is the product rule for derivatives utilizing the original function h(x) = f(x)g(x) ?
- H^'(x)= f^'(x)g^'(x)
- H^'(x)=f^'(x)g(x) - f(x)g^'(x)
- H^'(x)=f^'(x)g^'(x) + f(x)g(x)
- H^'(x)=f^'(x)g(x) + f(x)g^'(x)

About This Quiz

This quiz titled 'Chapter 12: Limits and Derivatives' evaluates understanding of calculus concepts such as product rule, quotient rule, power rule, and the basics of derivatives and antiderivatives. It's designed to enhance problem-solving skills and mathematical reasoning relevant to calculus studies.

Chapter 12 : Limits And Derivatives - Quiz

2.

2. Which of the following is the derivative of f(x)= x²+ x + 2 ?
- 2x
- X²+ x
- 2x + 1
- 0
Correct Answer

A. 2x + 1

Explanation

The derivative of a function represents the rate at which the function is changing at any given point. To find the derivative of f(x)= x^2 + x + 2, we can apply the power rule of differentiation. The power rule states that the derivative of x^n is n*x^(n-1). Applying this rule to each term of the function, we get the derivative of f(x) as 2x + 1. Therefore, the correct answer is 2x + 1.

Rate this question:
3.

3. Which of the following is the quotient rule for derivatives?
- H^'(x)=((g(x)f^'(x) + f(x)g^'(x)) / (g(x))²
- H^'(x)=((g^'(x)f^'(x) - f(x)g(x)) / (g(x))
- H^'(x)=((g(x)f^'(x) - f(x)g^'(x)) / (g(x))²
- H^'(x)=((g^'(x)f^'(x) + f(x)g(x)) / (g(x))
Correct Answer

A. H^'(x)=((g(x)f^'(x) - f(x)g^'(x)) / (g(x))²

Explanation

The quotient rule for derivatives states that the derivative of a quotient of two functions is equal to the numerator's derivative times the denominator minus the denominator's derivative times the numerator, all divided by the square of the denominator. Therefore, the correct answer is h'(x)=((g(x)f'(x) - f(x)g'(x)) / (g(x))^2.

Rate this question:
4.

4. What rule should be used in deriving f(x) = x⁵
- Constant rule
- Power rule
- Difference rule
- Sum rule
Correct Answer

A. Power rule

Explanation

The correct answer is Power rule. This rule states that when differentiating a function of the form f(x) = x^n, where n is a constant, the derivative is given by f'(x) = n*x^(n-1). In this case, the function f(x) = x^5 can be differentiated using the power rule to obtain f'(x) = 5*x^(5-1) = 5*x^4.

Rate this question:
5.

5. Another word for 'integral' is .. .
- Constant
- Derivative
- Theorem
- Antiderivative
Correct Answer

A. Antiderivative

Explanation

An antiderivative is a function that reverses the process of differentiation. It is the opposite of finding a derivative. In calculus, the antiderivative of a function is also known as the integral of the function. Therefore, the given word 'integral' is synonymous with 'antiderivative'.

Rate this question:
6.

6. What does C represent in an antiderivative?
- A variable
- A constant
- None
Correct Answer

A. A constant

Explanation

In the context of an antiderivative, the variable C represents a constant. When finding the antiderivative of a function, we add a constant term (C) to the solution because the derivative of a constant is always zero. This constant accounts for all possible solutions to the antiderivative equation.

Rate this question:
7.

8. What is the limit?
- 20
- 12
- Infinity
- DNE
Correct Answer

A. 20

Explanation

The limit refers to the value that a function approaches as the input approaches a certain value. In this case, the limit is 20, which means that as the input approaches a certain value, the function also approaches 20.

Rate this question:

1
8.
- A
- B
- C
- D
Correct Answer

A. D
9.
- 0
- 4/3
- -3/2
- Infinity
Correct Answer

A. Infinity
10.

10. ∫ 4 dx
- 4
- 4x + C
- 4t + C
- 2x² + C
Correct Answer

A. 4x + C

Explanation

The integral of 4 with respect to x is equal to 4x. The "+ C" represents the constant of integration, which is added because when taking the derivative of a constant, it becomes zero. Therefore, the correct answer is 4x + C.

Rate this question: