derivatives & integrals review Flashcards
(31 cards)
1
Q
d/dx [u +/- v] =
A
u’ +/- v’
1
Q
d/dx [cu] =
A
cu’
2
Q
d/dx [uv] =
A
uv’ + vu’
firstDsecond + secondDfirst
3
Q
d/dx [u/v] =
A
(vu’ - uv’) / v^2
loDhi - hiDlo / (lo)^2
4
Q
d/dx [c] =
A
0
c is a constant
5
Q
d/dx [u^n] =
A
nu^n-1(u’)
power rule
6
Q
d/dx [x] =
A
1
x has a power of one, so 1
7
Q
d/dx [ln u] =
A
u’ / u
8
Q
d/dx [e^u] =
A
e^u (u’)
9
Q
d/dx [sin u] =
A
(cos u) u’
10
Q
d/dx [cos u] =
A
- (sin u) u’
(negative sin u)
11
Q
d/dx [tan u] =
A
(sec^2 u) u’
12
Q
d/dx [cot u] =
A
- (csc^2 u) u’
negative (csc^2 u) u’
13
Q
d/dx [sec u] =
A
(sec u tan u) u’
14
Q
d/dx [csc u] =
A
- (csc u cot u) u’
15
Q
∫ k f(u) du =
A
k ∫ f(u) du
16
Q
∫ [f(u) +/- g(u)] du =
A
∫ f(u) du +/- ∫ g(u) du
17
Q
∫ du =
A
u + C
18
Q
∫ sin u du =
A
- cos u + C
19
Q
∫ cos u du =
A
sin u + C
20
Q
∫ sec^2 u du =
A
tan u + C
21
Q
∫ csc^2 u du =
A
- cot u + C
22
Q
∫ sec u tan u du =
A
sec u + C
23
Q
∫ csc u cot u du =
A
- csc u + C
25
∫ a^u du =
(1/ln a) a^u + C
26
∫ tan u du =
-ln |cos u| + C
27
∫ sec u du =
ln |sec u + tan u|+ C
28
∫ du / (a^2 + u^2) =
1/a arctan u/a + C
29
∫ du / sqrt (a^2 - u^2) =
arcsin u/a + C
30
∫ du/ u ( sqrt (u^2 - a^2))
1/arcsec (|u|/a) + C
31
∫ csc u du =
-ln |cscu + cotu| + C
