Differentiation and Integration Formulas Flashcards
1
Q
d(cu)
A
cu’
2
Q
d(u ± v)
A
u’ ± v’
3
Q
d(uv)
A
uv’ + vu’
4
Q
d(u/v)
A
(vu’ - uv’)/v^2
5
Q
d(c)
A
0
6
Q
d(u^n)
A
n(u^(n-1))(u’)
7
Q
d(x)
A
1
8
Q
d(abs(u))
A
u/abs(u) * (u’), u ≠ 0
9
Q
d(ln(u))
A
u’/u
10
Q
d(e^u)
A
(e^u)u’
11
Q
d(log(bs(a))u)
A
u’/(ln(a))u
12
Q
d(a^u)
A
(ln(a))(a^u)(u’)
13
Q
d(sin(u))
A
(cos(u))(u’)
14
Q
d(cos(u))
A
-(sin(u))(u’)
15
Q
d(tan(u))
A
(sec^2(u))(u’)
16
Q
d(cot(u))
A
-(csc^2(u))(u’)
17
Q
d(sec(u))
A
(sec(u)*tan(u))(u’)
18
Q
d(csc(u))
A
-(csc(u)*cot(u))(u’)
19
Q
d(arcsin(u))
A
u’/sqrt(1 - (u^2))
20
Q
d(arctan(u))
A
u’/(1+(u^2))
21
Q
∫kf(u)(du)
A
k∫f(u)(du)
22
Q
A
∫f(u)(du) ± ∫g(u)(du)
23
Q
∫(du)
A
u + C
24
Q
∫(u^n)(du)
A
[(u^(n+1))/(n + 1)] + C, n ≠ -1
25
∫(du)/u
ln(abs(u)) + C
26
∫(e^u)(du)
(e^u) + C
27
∫(a^u)(du)
[1/(ln(a)) * (a^u)] + C
28
∫sin(u)(du)
-cos(u) + C
29
∫cos(u)(du)
sin(u) + C
30
∫tan(u)(du)
-ln(abs(cos(u))) + C
31
∫cot(u)(du)
ln(abs(sin(u))) + C
32
∫sec(u)(du)
ln(abs(sec(u) + tan(u))) + C
33
∫csc(u)(du)
-ln(abs(csc(u) + cot(u))) + C
34
∫sec^2(u)(du)
tan(u) + C
35
∫csc^2(u)(du)
-cot(u) + C
36
∫sec(u)tan(u)(du)
sec(u) + C
37
∫csc(u)cot(u)(du)
-csc(u) + C
38
∫(du)/sqrt((a^2) - (u^2))
arcsin(u/a) + C
39
∫(du)/((a^2) + (u^2))
(1/a)arctan(u/a) + C
40
∫(e^ku)(du)
[(1/k)(e^ku)] + C
