derivatives and integrals Flashcards
1
Q
d/dx [cx]
A
cx’
2
Q
d/dx [xy]
A
xy’ + yx’
3
Q
d/dx [c]
A
0
4
Q
d/dx [x]
A
1
5
Q
d/dx [lnx]
A
1/x (x’)
6
Q
d/dx [loga x]
A
1/ln(a) (1/x) (x’)
7
Q
d/dx [sin x]
A
cos x (x’)
8
Q
d/dx [tan x]
A
sec²x (x’)
9
Q
d/dx [sec x]
A
secxtanx (x’)
10
Q
d/dx [arcsinx]
A
x’/(√1-x²)
11
Q
d/dx [arctanx]
A
x’/(1+x²)
12
Q
d/dx [arcsec]
A
x’/(|x|√x²-1)
13
Q
d/dx [x +/- y]
A
x’ +/- y’
14
Q
d/dx [x/y]
A
(yx’ - xy’)/y²
15
Q
d/dx [x^n]
A
nx^n-1x’
16
Q
d/dx [|x|]
A
x/|x| (x’) ; x CANNOT = 0
17
Q
d/dx [e^x]
A
e^x(x’)
18
Q
d/dx [a^x]
A
(ln a)(a^x)(x’)
19
Q
d/dx [cosu]
A
-sinx (x’)
20
Q
d/dx [cotx]
A
-csc²x (x’)
21
Q
d/dx [cscx]
A
-cscxcotx (x’)
22
Q
d/dx [arccosx]
A
-x’/(√1-x²)
23
Q
d/dx [arccotx]
A
-x’/(1+x²)
24
Q
d/dx [arccscx]
A
-x’/(|x|√x²-1)
25
∫ k f(x) dx
k ∫ f(x) dx
26
∫ dx
x + C
27
∫ 1/x dx
ln |x| + C
28
∫ a^x dx
(1/lna) (a^x) + C
29
∫ cosx dx
sinx + C
30
∫ cotx dx
ln|sinx| + C
31
∫ cscx dx
-ln|cscx + cotx| + C
32
∫ csc²x dx
-cotx + C
33
∫ cscxcotx dx
-cscx + C
34
∫ 1/(a²+x²) dx
1/a arctan x/a + C
35
∫ [f(x) +/- g(x)] dx
∫ f(x) dx +/- ∫ g(x) dx
36
∫ x^n dx
(x^n+1)/(n+1)
37
∫ e^x dx
e^x + C
38
∫ sinx dx
-cosx + C
39
∫ tanx dx
-ln|cosx| +C
40
∫ secx dx
ln|secx + tanx| + C
41
∫ sec²x dx
tanx + C
42
∫ secxtanx dx
secx + C
43
∫ 1/(√a²-x²) dx
arcsin x/a + C
44
∫ 1/(x√x²-a²) dx
(1/a) arcsec|x|/a +C
