Derivadas

Question 1

What is the derivative of sin(u)?

Answer 1

The derivative of sin(u) is cos(u).

Question 2

What is the derivative of cos(u)?

Answer 2

The derivative of cos(u) is -sin(u).

Question 3

What is the derivative of tan(u)?

Answer 3

The derivative of tan(u) is sec²(u).

Question 4

What is the derivative of cot(u)?

Answer 4

The derivative of cot(u) is -csc²(u).u’

Question 5

What is the derivative of sec(u)?

Answer 5

The derivative of sec(u) is sec(u)tan(u).

Question 6

What is the derivative of csc(u)?

Answer 6

The derivative of csc(u) is -csc(u)cot(u).

Question 7

True or False: The derivative of sin(u) is negative.

Answer 7

False.

Question 8

Fill in the blank: The derivative of _______ is -sin(u).

Answer 8

cos(u)

Question 9

What is the general formula for the derivative of sin(u)?

Answer 9

The derivative of sin(u) is cos(u).

Question 10

What is the relationship between the derivatives of tan(u) and sec(u)?

Answer 10

The derivative of tan(u) is sec²(u).u’, and the derivative of sec(u) is sec(u)tan(u).u’

Question 11

What is the derivative of sec(u)tan(u)?

Answer 11

The derivative of sec(u)tan(u) involves both sec(u) and sec²(u).

Question 12

Multiple Choice: Which of the following is the derivative of csc(u)? A) csc(u)cot(u) B) -csc(u)cot(u) C) sec(u)tan(u)

Answer 12

B) -csc(u)cot(u)

Question 13

What happens to the derivative of cot(u) when you differentiate it?

Answer 13

It becomes -csc²(u).

Question 14

True or False: The derivative of cos(u) is positive.

Answer 14

False.

Question 15

Fill in the blank: The derivative of tan(u) is _______.

Answer 15

sec²(u).u’

Question 16

What is the derivative of -sin(u)?

Answer 16

The derivative of -sin(u) is -cos(u).

Question 17

How do the derivatives of sine and cosine relate to each other?

Answer 17

The derivative of sin(u) is cos(u), and the derivative of cos(u) is -sin(u).

Question 18

What is the derivative of the function f(u) = csc(u)?

Answer 18

The derivative is -csc(u)cot(u).

Question 19

Multiple Choice: Which derivative is equal to sec²(u)? A) sin(u) B) tan(u) C) cos(u)

Answer 19

B) tan(u)

Question 20

What is the derivative of the function f(u) = sec(u)?

Answer 20

The derivative is sec(u)tan(u).

Question 21

Fill in the blank: The derivative of _______ is sec(u)tan(u).

Answer 21

sec(u)

Question 22

True or False: The derivative of csc(u) is positive.

Answer 22

False.

Question 23

What is the formula for the derivative of cot(u)?

Answer 23

The derivative of cot(u) is -csc²(u).

Question 24

What is the derivative of tan(u) with respect to u?

Answer 24

The derivative is sec²(u).

Question 25

What is the pattern of derivatives for trigonometric functions?

Answer 25

The derivatives cycle through sine, cosine, tangent, and their reciprocals with alternating signs.