Trig Derivatives

Question 1

What is the derivative of sin(x)?

Answer 1

cos(x)

Question 2

What is the derivative of cos(x)?

Answer 2

-sin(x)

Question 3

What is the derivative of tan(x)?

Answer 3

sec^2(x)

Question 4

What is the derivative of csc(x)?

Answer 4

-csc(x)cot(x)

Question 5

What is the derivative of sec(x)?

Answer 5

sec(x)tan(x)

Question 6

What is the derivative of cot(x)?

Answer 6

-csc^2(x)

Question 7

What is the derivative of arcsin(x)?

Answer 7

1/sqrt(1-x^2)

Question 8

What is the derivative of arccos(x)?

Answer 8

-1/sqrt(1-x^2)

Question 9

What is the derivative of arctan(x)?

Answer 9

1/(1+x^2)

Question 10

What is the derivative of arccsc(x)?

Answer 10

-1/(|x|sqrt(x^2-1))

Question 11

What is the derivative of arcsec(x)?

Answer 11

1/(|x|sqrt(x^2-1))

Question 12

What is the derivative of arccot(x)?

Answer 12

-1/(1+x^2)

Question 13

Fill in the blank: The derivative of csc(x) is _____ csc(x)cot(x).

Answer 13

-csc(x)

Question 14

What is the derivative of f(x) = sin^2(x)?

Answer 14

2sin(x)cos(x)

Question 15

What is the derivative of f(x) = cos^2(x)?

Answer 15

-2cos(x)sin(x)

Question 16

Find the derivative of f(x) = sec^2(x).

Answer 16

2sec^2(x)tan(x)

Question 17

What is the derivative of the inverse sine function?

Answer 17

1/sqrt(1-x^2)

Question 18

What is the derivative of the inverse tangent function?

Answer 18

1/(1+x^2)