Finals

Question 1

Derivative f(x) / g(x)

Answer 1

(g(x)f’(x) - f(x)g’(x))/ g(x)^2

Question 2

Derivative f(x)g(x)

Answer 2

f(x)g’(x) + g(x)f’(x)

Question 3

Derivative f(g(x))

Answer 3

f’(g(x)) * g’(x)

Question 4

Derivative cos(x)

Answer 4

-sin(x)

Question 5

Derivative sin(x)

Answer 5

cos(x)

Question 6

Derivative ln(u)

Answer 6

1/u

Question 7

Derivative tan(x)

Answer 7

sec^2(x)

Question 8

Derivative cot(x)

Answer 8

-csc^2(x)

Question 9

Derivative csc(x)

Answer 9

-csc(x)cot(x)

Question 10

Derivative sec(x)

Answer 10

sec(x)tan(x)

Question 11

Derivative e^u

Answer 11

U’e^u

Question 12

Derivative logau

Answer 12

u’ /ulna

Question 13

Derivative a^u

Answer 13

u’a^u * lna

Question 14

Integral u^n

Answer 14

u^(n+1) / n+1 +c

Question 15

Integral 1/u

Answer 15

ln(u) + c

Question 16

Integral e^u

Answer 16

e^u + c

Question 17

Integral sinu

Answer 17

-cosu + c

Question 18

Integral cosu

Answer 18

sinu + c

Question 19

Integral tanu

Answer 19

-ln(cosu) + c

Question 20

Integral cotu

Answer 20

ln(sinu) + c

Question 22

Derivative arctanu

Answer 22

u’/1+u^2

Question 22

Integral cscu

Answer 22

-ln(cscu + cotu) + c

Question 22

Integral secu

Answer 22

ln(secu + tanu) +c

Question 23

Derivative arccosu

Answer 23

-u’/√(1-u^2)

Question 23

Derivative arcsinu

Answer 23

u’/ √(1-u^2)

Question 24

Derivative arccotu

Answer 24

-u’/1+u^2

Question 25

Inverse Steps

Answer 25

1. Set function = to x-value and solve
2. Plug that answer into f’(x)
3. Take reciprocal

Question 26

ln(1) =

Answer 26

0

Question 27

ln(ab)

Answer 27

ln(a) + ln(b)

Question 28

ln(a/b)

Answer 28

ln(a) - ln(b)

Question 29

Fundamental Theorem of Calc

Answer 29

Integral a to b f(x) = f(b) - f(a)

Question 30

MVT for integrals

Answer 30

1/(b - a) Integral a to b of f(x)

Question 31

Average Value for integrals

Answer 31

1(b - a) Integral a to b of f(x) solve for c

Question 32

2nd Fundamental Theorem of Calc

Answer 32

f(b) * b’ - f(a) * a’

Question 33

Use 2nd ftoc when

Answer 33

taking the derivative of an integral

Question 34

Trapezoidal Sum Estimation

Answer 34

.5 * w * (1a + 2b + 2c +1d)

Question 35

Riemann Sum Estimation

Answer 35

w * all values except rightmost or leftmost value

Question 36

Midpoint Rectangle Estimation

Answer 36

w * points in between left and right added together

Question 37

Use finding areas of shapes when

Answer 37

you’re solving an integral when you don’t know the equation

Question 38

square cross section

Answer 38

integral s^2

Question 39

equilateral triangle cross section

Answer 39

√3/4 integral s^2

Question 40

isosceles right triangle cross section

Answer 40

1/2 integral s^2

Question 41

semicircle cross section

Answer 41

1/8 integral s^2

Question 42

Rectangle cross section

Answer 42

k integral s^2

Question 43

Washer method (for gaps)

Answer 43

pi integral R(x)^2 - r(x)^2

Question 44

Disk method (no gap)

Answer 44

pi integral (R(x))^2

Question 45

Exponential growth equation

Answer 45

f(x) = a(1 + r)^2