Differentiation Basic Rules Quiz

Approved & Edited by ProProfs Editorial Team

The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.

Learn about Our Editorial Process

| By Themes

Themes

Community Contributor

Quizzes Created: 420 | Total Attempts: 915,136

Questions: 10 | Attempts: 796 | Updated: Mar 21, 2023

Questions

Settings

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Play as

Quiz Flashcard

Create your own Quiz

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

Check out our online quiz and test your understanding of Differentiation concepts, rules, and solve some simple questions for us.

Questions and Answers

1.

Differentiate y=3x⁴-5x
- A.
  
  3x³-5
- B.
  
  12x³-5
- C.
  
  12x³+5
- D.
  
  12x²
Correct Answer
B. 12x³-5

Explanation
The correct answer is 12x3-5. This is the correct answer because when we differentiate the given function y=3x4-5x, we apply the power rule of differentiation which states that when differentiating a term with a variable raised to a power, we multiply the coefficient by the power and then decrease the power by 1. Therefore, when we differentiate 3x4, we get 12x3, and when we differentiate -5x, we get -5. Thus, the derivative of y=3x4-5x is 12x3-5.

Rate this question:

1
0
2.

Is differentiation of y=6x³-1 is 18x³ true or false?
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The differentiation of y=6x^3-1 is not equal to 18x^3. When we differentiate y=6x^3-1, the power rule states that the derivative of x^n is nx^(n-1). Therefore, the derivative of 6x^3 is 18x^2, not 18x^3.

Rate this question:

1
0
3.

Differentiate y=5/x²
- A.
  
  5x²
- B.
  
  -5x^-3
- C.
  
  -10x^-3
- D.
  
  10x^-3
- E.
  
  Option 5
Correct Answer
C. -10x^-3

Explanation
The given expression is y = 5/x^2. To differentiate this expression, we use the power rule of differentiation. The power rule states that when differentiating a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1). Applying this rule, we differentiate y = 5/x^2 as follows:
y' = (5)(-2)x^(-2-1) = -10x^(-3) = -10/x^3. Therefore, the correct answer is -10x-3.

Rate this question:

3
0
4.

Differentiate y= -3x^-5-10x+2
- A.
  
  3x⁵-10x
- B.
  
  -3x^-6+10
- C.
  
  15x^-6-10
- D.
  
  15x^-5-10
Correct Answer
C. 15x^-6-10

Explanation
The given expression is a polynomial with two terms. To differentiate it, we can use the power rule, which states that the derivative of x^n is n*x^(n-1). Applying this rule to the first term, -3x, we get -3. For the second term, -10x, the derivative is -10. Therefore, the derivative of the given expression is 15x - 3 - 10, which simplifies to 15x - 6 - 10.

Rate this question:

2
0
5.

Differentiate y=3x^-4+6x-1
- A.
  
  12x-1
- B.
  
  -4x^-5+6x-1
- C.
  
  12x^-5+6
- D.
  
  -12x^-5+6
- E.
  
  Option 5
Correct Answer
D. -12x^-5+6

Explanation
The given expression is y=3x-4+6x-1. We can simplify this expression by combining like terms. Combining 3x and 6x, we get 9x. Combining -4 and -1, we get -5. Therefore, the simplified expression is 9x - 5. The answer -12x-5+6 does not match the simplified expression, so it is not the correct answer.

Rate this question:
6.

Differentiate y=5-13x²-4x³
- A.
  
  26x-12x
- B.
  
  -26x-12x²
- C.
  
  -13x²-12x
- D.
  
  26x²-12
- E.
  
  Option 5
Correct Answer
B. -26x-12x²

Explanation
The given expression is y=5-13x^2-4x^3. To differentiate this expression, we take the derivative of each term. The derivative of 5 is 0, the derivative of -13x^2 is -26x, and the derivative of -4x^3 is -12x^2. Therefore, the differentiated expression is -26x-12x^2.

Rate this question:

1
0
7.

Is differentiation of y=5x^-2-12 is -10x^-3 true or false?
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The given expression y=5x-2-12 can be simplified as y=5x-14. Therefore, the correct answer -10x-3 is false.

Rate this question:

1
0
8.

Differentiate y=4/x⁴
- A.
  
  4x^-5
- B.
  
  4x⁵
- C.
  
  16x^-5
- D.
  
  -16x^-5
Correct Answer
D. -16x^-5

Explanation
The given expression is y = 4/x^4 - 4x - 5. To differentiate this expression, we can use the power rule for differentiation. The derivative of 4/x^4 is -16/x^5, the derivative of -4x is -4, and the derivative of -5 is 0. Combining these derivatives, we get -16/x^5 - 4. Simplifying further, we can rewrite this as -16x^-5 - 4, which is equivalent to -16/x^5 - 4. Therefore, the correct answer is -16x - 5.

Rate this question:

1
0

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
Mar 26, 2021

Quiz Created by
Themes

Differentiation Basic Rules Quiz

Differentiate y=3x4-5x

Is differentiation of y=6x3-1 is 18x3 true or false?

Differentiate y=5/x2

Differentiate y= -3x-5-10x+2

Differentiate y=3x-4+6x-1

Differentiate y=5-13x2-4x3

Is differentiation of y=5x-2-12 is -10x-3 true or false?

Differentiate y=4/x4

Differentiate y=3x⁴-5x

Is differentiation of y=6x³-1 is 18x³ true or false?

Differentiate y=5/x²

Differentiate y= -3x^-5-10x+2

Differentiate y=3x^-4+6x-1

Differentiate y=5-13x²-4x³

Is differentiation of y=5x^-2-12 is -10x^-3 true or false?

Differentiate y=4/x⁴