Inverse Trig

Question 1

What is the derivative of arcsin(x)?

Answer 1

d/dx arcsin(x) = 1 / √(1 - x²)

Question 2

What is the derivative of arccos(x)?

Answer 2

d/dx arccos(x) = -1 / √(1 - x²)

Question 3

What is the derivative of arctan(x)?

Answer 3

d/dx arctan(x) = 1 / (1 + x²)

Question 4

What is the derivative of arcsec(x)?

Answer 4

d/dx arcsec(x) = 1 / |x|√(x² - 1)

Question 5

What is the derivative of arccsc(x)?

Answer 5

d/dx arccsc(x) = -1 / |x|√(x² - 1)

Question 6

What is the derivative of arc cot(x)?

Answer 6

d/dx arccot(x) = -1 / (1 + x²)

Question 7

True or False: The derivative of arcsin(x) is negative.

Answer 7

False

Question 8

Fill in the blank: d/dx arccos(x) = _____

Answer 8

-1 / √(1 - x²)

Question 9

What is the formula for the derivative of arctan(x)?

Answer 9

d/dx arctan(x) = 1 / (1 + x²)

Question 10

Multiple choice: What is d/dx arcsec(x)? A) 1 / √(x² - 1) B) 1 / |x|√(x² - 1) C) 1 / (1 + x²)

Answer 10

B) 1 / |x|√(x² - 1)