AP Calculus derivatives Review

Question 1

The first derivative of a function provides information about the _______ of that function.

Accepted Answer

inc/dec and max/min

Question 2

Choose the correct answer: (d/dx)[sec(u)] =

Accepted Answer

sec(u)tan(u)·u'

Question 3

Choose the correct answer: (d/dx)[vu] =

Accepted Answer

uv' + vu'

Question 4

Choose the correct answer: (d/dx)[cot(u)] =

Accepted Answer

-csc2(u)·u'

Question 5

Choose the correct answer: (d/dx)[ln(u)] =

Accepted Answer

(1/u)·u'

Question 6

Choose the correct answer: (d/dx)[csc(u)] =

Accepted Answer

-csc(u)cot(u)·u'

Question 7

Choose the correct answer: (d/dx)[sec(u)] =

Accepted Answer

sec(u)tan(u)·u'

Question 8

Choose the correct answer.

Accepted Answer

-6x2sin(x3)cos(x3)

Question 9

Choose the correct answer: (d/dx)[u/v] =

Accepted Answer

(vu' - uv')/(v2)

Question 10

The second derivative of a function provides information about the _______ of that function.

Accepted Answer

concavity

Question 11

Choose the correct answer: (d/dx)[tan(u)] =

Accepted Answer

sec2(u)·u'

Question 12

Choose the correct answer: (d/dx)[eu] =

Accepted Answer

eu·u'

Question 13

Choose the correct answer: (d/dx)[sin(u)] =

Accepted Answer

cos(u)·u'

Question 14

Choose the correct answer: (d/dx)[au] =

Accepted Answer

au·ln(a)·u'

Question 15

Choose the correct answer: (d/dx)[cos(u)] =

Accepted Answer

-sin(u)·u'

Questions 15