#2: Derivatives of Inverse Trig Functions

Question 1

What is the derivative of the inverse sine function, sin^(-1)(x)?

Answer 1

The derivative is 1 / √(1 - x^2).

Question 2

True or False: The derivative of the inverse cosine function, cos^(-1)(x), is -1 / √(1 - x^2).

Answer 2

True.

Question 3

Fill in the blank: The derivative of the inverse tangent function, tan^(-1)(x), is ____.

Answer 3

1 / (1 + x^2).

Question 4

What is the formula for the derivative of the inverse cotangent function, cot^(-1)(x)?

Answer 4

-1 / (1 + x^2).

Question 5

Multiple Choice: What is the derivative of the inverse secant function, sec^(-1)(x)?
A) 1 / (|x|√(x^2 - 1))
B) -1 / (|x|√(x^2 - 1))
C) 1 / (x√(x^2 - 1))

Answer 5

A) 1 / (|x|√(x^2 - 1)).

Question 6

What is the derivative of the inverse cosecant function, csc^(-1)(x)?

Answer 6

-1 / (|x|√(x^2 - 1)).

Question 7

True or False: The derivatives of inverse trigonometric functions are defined for all real numbers.

Answer 7

False.

Question 8

What is the domain of the function sin^(-1)(x)?

Answer 8

The domain is [-1, 1].

Question 9

Short Answer: State the relationship between the derivatives of inverse sine and inverse cosine functions.

Answer 9

They are negatives of each other.

Question 10

Multiple Choice: Which of the following is the derivative of y = cos^(-1)(x)?
A) 1 / √(1 - x^2)
B) -1 / √(1 - x^2)
C) 1 / (1 + x^2)

Answer 10

B) -1 / √(1 - x^2).