Finals Flashcards
(49 cards)
1
Q
Derivative f(x) / g(x)
A
(g(x)f’(x) - f(x)g’(x))/ g(x)^2
2
Q
Derivative f(x)g(x)
A
f(x)g’(x) + g(x)f’(x)
3
Q
Derivative f(g(x))
A
f’(g(x)) * g’(x)
4
Q
Derivative cos(x)
A
-sin(x)
5
Q
Derivative sin(x)
A
cos(x)
6
Q
Derivative ln(u)
A
1/u
7
Q
Derivative tan(x)
A
sec^2(x)
8
Q
Derivative cot(x)
A
-csc^2(x)
9
Q
Derivative csc(x)
A
-csc(x)cot(x)
10
Q
Derivative sec(x)
A
sec(x)tan(x)
11
Q
Derivative e^u
A
U’e^u
12
Q
Derivative logau
A
u’ /ulna
13
Q
Derivative a^u
A
u’a^u * lna
14
Q
Integral u^n
A
u^(n+1) / n+1 +c
15
Q
Integral 1/u
A
ln(u) + c
16
Q
Integral e^u
A
e^u + c
17
Q
Integral sinu
A
-cosu + c
18
Q
Integral cosu
A
sinu + c
19
Q
Integral tanu
A
-ln(cosu) + c
20
Q
Integral cotu
A
ln(sinu) + c
21
Q
A
21
Q
A
22
Q
Derivative arctanu
A
u’/1+u^2
22
Q
Integral cscu
A
-ln(cscu + cotu) + c
22
Integral secu
ln(secu + tanu) +c
23
Derivative arccosu
-u'/√(1-u^2)
23
Derivative arcsinu
u'/ √(1-u^2)
24
Derivative arccotu
-u'/1+u^2
25
Inverse Steps
1. Set function = to x-value and solve
2. Plug that answer into f'(x)
3. Take reciprocal
26
ln(1) =
0
27
ln(ab)
ln(a) + ln(b)
28
ln(a/b)
ln(a) - ln(b)
29
Fundamental Theorem of Calc
Integral a to b f(x) = f(b) - f(a)
30
MVT for integrals
1/(b - a) Integral a to b of f(x)
31
Average Value for integrals
1(b - a) Integral a to b of f(x) solve for c
32
2nd Fundamental Theorem of Calc
f(b) * b' - f(a) * a'
33
Use 2nd ftoc when
taking the derivative of an integral
34
Trapezoidal Sum Estimation
.5 * w * (1a + 2b + 2c +1d)
35
Riemann Sum Estimation
w * all values except rightmost or leftmost value
36
Midpoint Rectangle Estimation
w * points in between left and right added together
37
Use finding areas of shapes when
you're solving an integral when you don't know the equation
38
square cross section
integral s^2
39
equilateral triangle cross section
√3/4 integral s^2
40
isosceles right triangle cross section
1/2 integral s^2
41
semicircle cross section
1/8 integral s^2
42
Rectangle cross section
k integral s^2
43
Washer method (for gaps)
pi integral R(x)^2 - r(x)^2
44
Disk method (no gap)
pi integral (R(x))^2
45
Exponential growth equation
f(x) = a(1 + r)^2
