Differentiation and Integration Rules Flashcards
1
Q
d/dx of cu
A
cu’
2
Q
d/dx u +/- v
A
u’ +/- v’
3
Q
d/dx uv
A
uv’ + vu’
4
Q
d/dx u/v
A
vu’-uv’ all over v^2
5
Q
d/dx c
A
0
6
Q
d/dx u^n
A
n * u^n-1 * u’
7
Q
d/dx x
A
1
8
Q
d/dx |u|
A
u/|u| * u’ (u not equal to 0)
9
Q
d/dx Ln u
A
1/u * u’
10
Q
d/dx e^u
A
e^u * u’
11
Q
d/dx logaU
A
1/Ln a * 1/u *u’
12
Q
d/dx a^u
A
Ln a * a^u * u’
13
Q
d/dx sin u
A
Cos u * u’
14
Q
d/dx cos u
A
-sin u *u’
15
Q
d/dx tan u
A
Sec^2 u *u’
16
Q
d/dx Cot u
A
-Csc^2 u * u’
17
Q
d/dx sec u
A
Sec u * tan u * u’
18
Q
d/dx Csc u
A
-Csc u * cot u * u’
19
Q
d/dx arcsin u
A
1/Square root of 1-u^2
Times u’
20
Q
d/dx arccos u
A
-1/Square root of 1-u^2
Times u’
21
Q
d/dx arctan u
A
1/1+u^2 * u’
22
Q
d/dx arccot u
A
-1/1+u^2 * u’
23
Q
d/dx arcsec u
A
1/absolute value of u * 1/Square root of u^2-1 *u’
24
Q
d/dx arccsc u
A
-1/absolute value of u * 1/Square root of u^2-1 *u’
25
{k*f(u)
K{f(u)
26
{f(u)+/-g(u)
{f(u) +/- {g(u)
27
{du
U + C
28
{u^n
1/n+1 * u^n+1 + C (n not equal to -1)
29
{du/u
Ln |u| + C
30
{e^u du
E^u + C
31
{a^u de
1/Ln a * a^u + C
32
{sin u du
-cos u + C
33
{cos u du
Sin u + C
34
{tan u du
-ln|cos u| + C
35
{cot u du
Ln|sin u| + C
36
{sec u du
Ln|sec u + tan u| + C
37
{csc u du
-ln|csc u + cot u| +C
38
{du/Square root of a^2-u^2
Arc sin u/a + C
39
{du/a^2+u^2
1/a arctan u/a + C
40
{du/u*Square root of u^2-a^2
1/a arcsec |u|/a + C
41
{Sec^2 u du
Tan u + C
42
{Csc^2 u du
-Cot u +C
43
{Sec u * tan u du
Sec u + C
44
{Csc u * cot u du
-Csc u + C
45
{Y'=ky
Y=Ce^kx
46
{Y'=ky(1-y/L)
Y=L/(1+be^-kt)
47
The integration of udv
U*V minus the integration of vdu
