Trig Derivatives Memorization 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 KenArrari

KenArrari

Community Contributor

Quizzes Created: 1 | Total Attempts: 5,415

Questions: 12 | Attempts: 5,492 | Updated: Aug 18, 2023

Questions

Settings

Create your own Quiz

Trig Derivatives Memorization Quiz. - Quiz

Nothing but absolute mindless memorization of the trig derivatives. Keep taking it until you have them memorized.

Questions and Answers

1.

Y=sin(x)
- A.
  
  Y'= sin(x)
- B.
  
  Y'= cos(x)
- C.
  
  Y'= tan(x)
- D.
  
  Y'=1/(1+x^2)
Correct Answer
B. Y'= cos(x)

Explanation
The derivative of sin(x) is cos(x).

Rate this question:
2.

Y= cos (x)
- A.
  
  Y'= sin(x)
- B.
  
  Y'= -sin(x)
- C.
  
  Y'= cot (x)
- D.
  
  Y'= sec (x)
Correct Answer
B. Y'= -sin(x)

Explanation
The derivative of the cosine function, y = cos(x), is equal to the negative sine function, y' = -sin(x). This can be derived using the chain rule of differentiation.

Rate this question:
3.

Y= tan(x)
- A.
  
  Y'= csc(x)
- B.
  
  Y'= cot(x)
- C.
  
  Y'= sec^2(x)
- D.
  
  Y'= -cscxCotx
Correct Answer
C. Y'= sec^2(x)

Explanation
The derivative of y = tan(x) is y' = sec^2(x). This is because the derivative of tan(x) is equal to the derivative of sin(x)/cos(x), which can be rewritten as 1/cos^2(x). Since 1/cos^2(x) is equivalent to sec^2(x), the correct answer is y' = sec^2(x).

Rate this question:
4.

Y= sec(x)
- A.
  
  Y'= 1/(1+x^2)
- B.
  
  Y'= -csc^2(x)
- C.
  
  Y'= -cos(x)
- D.
  
  Y'= Sec(x)Tan(x)
Correct Answer
D. Y'= Sec(x)Tan(x)

Explanation
The derivative of y = sec(x) is y' = sec(x)tan(x). This can be derived using the quotient rule, where the derivative of sec(x) is sec(x)tan(x) and the derivative of tan(x) is sec^2(x). Therefore, the correct answer is y' = sec(x)tan(x).

Rate this question:
5.

Y= cot(x)
- A.
  
  Y'=-csc^2(x)
- B.
  
  Y'= -cos(x)
- C.
  
  Y'= -sin(x)
- D.
  
  Y'= sec(x)tan(x)
Correct Answer
A. Y'=-csc^2(x)

Explanation
The derivative of y=cot(x) is y'=-csc^2(x). This is because the derivative of cot(x) can be found using the quotient rule, where the derivative of the numerator is -csc^2(x) and the derivative of the denominator is 1. Therefore, the derivative of cot(x) is -csc^2(x).

Rate this question:
6.

Y= csc(x)
- A.
  
  Y'= Csc(x)
- B.
  
  Y'=-Csc(x)Cot(x)
- C.
  
  Y'= cot(x)tan(x)
- D.
  
  Y'= Sec(x)Tan(x)
Correct Answer
B. Y'=-Csc(x)Cot(x)

Explanation
The correct answer is y'=-Csc(x)Cot(x). The derivative of y = csc(x) can be found using the chain rule. The derivative of csc(x) is -csc(x)cot(x), where -csc(x) represents the derivative of the outer function and cot(x) represents the derivative of the inner function. Therefore, the correct answer is y'=-Csc(x)Cot(x).

Rate this question:
7.

Y= Sin^-1(x)
- A.
  
  Y'=1/√(1-x^2)
- B.
  
  Y'=-1/√(1-x^2)
Correct Answer
A. Y'=1/√(1-x^2)

Explanation
The given function is y = sin^(-1)(x), which represents the inverse sine function. To find the derivative of this function, we can use the chain rule. The derivative of sin^(-1)(x) is 1/√(1-x^2). Therefore, the correct answer is y' = 1/√(1-x^2).

Rate this question:

1
0
8.

Y= Tan^-1(x)
- A.
  
  Y'=1/√(1-x^2)
- B.
  
  Y'= 1/(1+x^2)
- C.
  
  Y'= -1/(1+x^2)
- D.
  
  Y'=1/√(1-x^2)
Correct Answer
B. Y'= 1/(1+x^2)

Explanation
The given function is y = Tan^-1(x), which represents the inverse tangent of x. The derivative of the inverse tangent function is 1/(1+x^2). This can be derived using the chain rule and the derivative of the tangent function. Therefore, the correct answer is y' = 1/(1+x^2).

Rate this question:

1
2
9.

Y= Sec^-1(x)
- A.
  
  Y'=1/√(1-x^2)
- B.
  
  Y'= 1/(1+x^2)
- C.
  
  Y'= -1/(x√(1-x^2)
- D.
  
  Y'= 1/(x√(1-x^2)
Correct Answer
D. Y'= 1/(x√(1-x^2)

Explanation
The given expression is y = Sec^-1(x), which represents the inverse secant function. To find the derivative of this function, we can use the chain rule. The derivative of Sec^-1(x) is equal to 1 divided by the square root of (1 - x^2). Therefore, the correct answer is y' = 1/(x√(1-x^2)).

Rate this question:

0
2
10.

Y= Cos^-1(x)
- A.
  
  Y'= 1/√(1-x^2)
- B.
  
  Y'= 1/(1+x^2)
- C.
  
  Y'= -1/(1+x^2)
- D.
  
  Y'= -1/√(1-x^2)
Correct Answer
D. Y'= -1/√(1-x^2)

Explanation
The given correct answer is y' = -1/√(1-x^2). This can be derived using the chain rule of differentiation. The derivative of y = Cos^-1(x) with respect to x can be found by differentiating the inverse cosine function. Applying the chain rule, we have y' = -1/√(1-x^2), which matches the given correct answer.

Rate this question:

1
0
11.

Y= cot^-1(x)
- A.
  
  Y'= -1/(1+x^2)
- B.
  
  Y'= 1/(1+x^2)
- C.
  
  Y'= -1/√(1-x^2)
- D.
  
  Y'= 1/√(1-x^2)
Correct Answer
A. Y'= -1/(1+x^2)

Explanation
The given correct answer is y' = -1/(1+x^2). This can be derived using the chain rule of differentiation. The derivative of cot^-1(x) can be found by differentiating the inverse cotangent function. The derivative of cot^-1(x) is equal to -1/(1+x^2). Therefore, the correct answer is y' = -1/(1+x^2).

Rate this question:
12.

Y= csc^-1(x)
- A.
  
  Y'= -1/(x√(1-x^2)
- B.
  
  Y'= -1/√(1-x^2)
- C.
  
  Y'= 1/(1+x^2)
- D.
  
  Y'= 1/(x√(1-x^2)
Correct Answer
A. Y'= -1/(x√(1-x^2)

Explanation
The given answer, y' = -1/(x√(1-x^2), is the derivative of the function y = csc^-1(x). This can be determined using the chain rule and the derivative of the inverse cosecant function. The derivative of csc^-1(x) is equal to -1/(x√(1-x^2), which matches the given answer.

Rate this question:

Trig Derivatives Memorization Quiz.

Y=sin(x)

Y= cos (x)

Y= tan(x)

Y= sec(x)

Y= cot(x)

Y= csc(x)

Y= Sin^-1(x)

Y= Tan^-1(x)

Y= Sec^-1(x)

Y= Cos^-1(x)

Y= cot^-1(x)

Y= csc^-1(x)