Derivatives Flashcards
1
Q
arctan(0)
A
0
2
Q
arctan(1)
A
pi/4
3
Q
(e^x)’
A
e^x
4
Q
(x^a)’
A
ax^a-1
5
Q
(lnx)’
A
1/x
6
Q
(sinx)’
A
cosx
7
Q
(cosx)’
A
-sinx
8
Q
(tgx)’
A
1/cos^2 x
9
Q
(arctgx)’
A
1/(x^2 +1)
10
Q
(arcsinx)’
A
1/√1-X^2
11
Q
(a^x)’
A
a^x lna
12
Q
(sin(1/x))’
A
-cos(1/x)/x^2
lebo
von(dnu)’*dnu’
13
Q
(f(g))’
A
f’(g)*g’
14
Q
(f*g)’
A
f’g+fg’
15
Q
(f/g)’
A
(f’g - fg’)/g^2
16
Q
(f+g)’
A
f’+g’
17
Q
(sin(3x))’
A
cos3x*3
18
Q
∫sin(x)
A
-cos(x)
19
Q
∫3^x lnx
A
3^x
20
Q
∫a^x lna
A
a^x
21
Q
1 =
A
sin^2x+cos^2x
22
Q
cos^2x=
A
1-sin^2x
23
Q
sin^2x
A
1-cos^2x
24
Q
tg=
A
sin/cos
25
ctg=
cos/sin
26
sec=
1/sin
27
cosec=
1/cos
28
sin2x=
2sinx*cosx
29
cos2x=
cos^2x-sin^2x
30
sin(a+-b)=
sina cosb +- cosa sinb
Znamienko vstrede ostava
31
cos(a+-b)=.
cosa cosb -+ sina sinb
pozor! znamiekno v strede sa bim bam bum meni sup hop a je to inak naopak
32
podielove kriterium
lim Un+1 / Un
q > 1 Divergentna
q < 1 Konvergentna
q = 1 na picu
33
mocninove kriterium
lim nroot(Un)
34
Integracne kriterium
Int{1-inf}(Un dn)
ked existuje: konverguje
35
neabsolutna konvergencia
musi platit minimalne:
lim Un = 0
36
iterujuca rada
iterujuca rada absolutne konverguje ked plati lim(|Un|) = 0
| ale stale moze byt neabsolutne konvergujuca ked sa nerovna 0
37
ln(e)
1
38
ln(1/e)
-1
39
∫sin(x/2)
-2cos(x/2)
40
∫e^2x
1/2 e^2x
