Derivatives

Question 1

derivative of a^x

Answer 1

X^a log a

Question 2

derivative of sinx

Answer 2

Cos x

Question 3

derivative of cos x

Answer 3

-sinx

Question 4

derivative of tanx

Answer 4

Sec²x

Question 5

derivative of cotx

Answer 5

-cosec²x

Question 6

derivative of sec x

Answer 6

Sec x(tan x)

Question 7

derivative of cosec x

Answer 7

-Cosec x(cot x)

Question 8

What is the derivative of sin(x)?

Answer 8

cos(x)

Question 9

What is the derivative of cos(x)?

Answer 9

-sin(x)

Question 10

True or False: The derivative of tan(x) is sec^2(x).

Answer 10

True

Question 11

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

Answer 11

-csc(x)cot(x)

Question 12

What is the derivative of sec(x)?

Answer 12

sec(x)tan(x)

Question 13

What is the derivative of cot(x)?

Answer 13

-csc^2(x)

Question 14

Which function’s derivative is -sin(x)?

Answer 14

cos(x)

Question 15

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

Answer 15

2cos(2x)

Question 16

Multiple choice: What is the derivative of f(x) = 3sin(x)? A) 3cos(x) B) 3sin(x) C) 3sec(x)

Answer 16

A) 3cos(x)

Question 17

What is the derivative of f(x) = 5tan(x)?

Answer 17

5sec^2(x)

Question 18

True or False: The derivative of sin^2(x) is 2sin(x)cos(x).

Answer 18

True

Question 19

What is the chain rule applied to sin(g(x))?

Answer 19

cos(g(x))g’(x)

Question 20

Fill in the blank: The derivative of cos(3x) is ______.

Answer 20

-3sin(3x)

Question 21

What is the second derivative of sin(x)?

Answer 21

-sin(x)

Question 22

Which trigonometric function has a derivative that is always positive?

Answer 22

tan(x)

Question 23

What is the derivative of f(x) = 4cos(x)?

Answer 23

-4sin(x)

Question 24

True or False: The derivative of a constant is zero.

Answer 24

True

Question 25

Fill in the blank: The derivative of sec^2(x) is ______.

Answer 25

2sec^2(x)tan(x)

Question 26

What is the derivative of f(x) = 7csc(x)?

Answer 26

-7csc(x)cot(x)

Question 27

What is the derivative of tan(2x)?

Answer 27

2sec^2(2x)

Question 28

Multiple choice: What is the derivative of f(x) = 2sin(x) + 3cos(x)? A) 2cos(x) - 3sin(x) B) 2sin(x) + 3cos(x) C) -2sin(x) + 3cos(x)

Answer 28

A) 2cos(x) - 3sin(x)

Question 29

What is the derivative of f(x) = arcsin(x)?

Answer 29

1/sqrt(1 - x^2)

Question 30

What is the derivative of f(x) = arccos(x)?

Answer 30

-1/sqrt(1 - x^2)

Question 31

True or False: The derivative of arctan(x) is 1/(1 + x^2).

Answer 31

True

Question 32

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

Answer 32

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

Question 33

What is the derivative of arccot(x)?

Answer 33

-1/(1 + x^2)