Inverse Trig Shortcuts

Question 1

What is the derivative of arcsin(x)?

Answer 1

1 / √(1 - x²)

Question 2

True or False: The derivative of arccos(x) is -1 / √(1 - x²).

Answer 2

True

Question 3

Fill in the blank: The derivative of arctan(x) is ______.

Answer 3

1 / (1 + x²)

Question 4

What is the derivative of arccot(x)?

Answer 4

-1 / (1 + x²)

Question 5

Multiple Choice: Which of the following is the derivative of arcsec(x)?
A) 1 / (|x|√(x² - 1))
B) -1 / (|x|√(x² - 1))
C) 1 / (√(x² - 1))

Answer 5

A) 1 / (|x|√(x² - 1))

Question 6

What is the derivative of arccsc(x)?

Answer 6

-1 / (|x|√(x² - 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 range of the function arcsin(x)?

Answer 8

-π/2 to π/2

Question 9

Fill in the blank: The derivative of arctan(kx) is ______, where k is a constant.

Answer 9

k / (1 + (kx)²)

Question 10

Short Answer: Provide the formula for the derivative of arcsec(x).

Answer 10

1 / (|x|√(x² - 1))