differentiation & integration REVIEW Flashcards
1
Q
d/dx [cu] =
A
cu’
2
Q
d/dx [u/v] =
A
vu’ - uv’ / v^2
3
Q
d/dx [x] =
A
1
4
Q
d/dx [e^u] =
A
e^u * u’
5
Q
d/dx [sin u] =
A
(cos u)u’
6
Q
d/dx [cot u] =
A
-(csc^2 u) u’
7
Q
d/dx [arcsin u] =
A
u’ / ( sqrt (1-u^2))
8
Q
d/dx [arccot u]=
A
-u’ / (1+u^2)
9
Q
d/dx [u +/- v] =
A
u’ +/- v’
10
Q
d/dx [c] =
A
0
11
Q
d/dx [log(base a) u] =
A
u’ / (ln a) u
12
Q
d/dx [cos u] =
A
-(sin u) u’
13
Q
d/dx [arccos u] =
A
-u’ / (sqrt (1-u^2))
{same as arcsin u, but neg}
14
Q
d/dx [arcsec u] =
A
u’ / (|u| (sqrt (u^2 -1))
15
Q
d/dx [uv] =
A
uv’ + vu’
16
Q
d/dx [u^n] =
A
power rule =
nu^(n-1) (u’)
17
Q
d/dx [ln u] =
A
u’ / u
18
Q
d/dx [a^u]
A
(ln a)a^u (u’)
19
Q
d/dx [tan u] =
A
(sec^2 u)u’
20
Q
d/dx [csc u] =
A
- (csc u cot u)u’
21
Q
d/dx [sec u] =
A
(sec u tan u)u’
22
Q
d/dx [arctan u] =
A
u’ / (1+u^2)
23
Q
d/dx [arcsec u] =
A
NEG (u’ / (|u| (sqrt (u^2 -1)) )
24
Q
∫ k f(u) du =
A
k ∫f(u) du
25
∫ du =
u + C
26
∫e^u du =
e^u + C
27
∫cos u du =
sin u + C
28
∫cot u du =
ln |sin u| + C
29
∫csc u du =
-ln|csc u + cot u| + C
30
∫csc^2 u du =
-cot u + C
31
∫ cscu cotu du =
-csc u + C
32
∫du / a^2 + u^2 =
1/a arctan u/a + C
33
∫ [f(u) +/- g(u)] du =
∫ f(u) du +/- ∫ g(u) du
34
∫a^u du
(1/ln a) a^u + C
35
∫ sinu du =
-cos u + C
36
∫ tanu du =
-ln |cos u| + C
37
∫secu du =
ln |sec u + tan u| + C
38
∫ sec^2 u du =
tan u + C
39
∫ sec u tan u du =
sec u + C
40
∫ du / (sqrt (a^2 - u^2))
arcsin u/a + C
41
∫du / (u (sqrt (u^2 - a^2))
1/a arcsec |u|/a + C
