Derivatives Flashcards
arctan(0)
0
arctan(1)
pi/4
(e^x)’
e^x
(x^a)’
ax^a-1
(lnx)’
1/x
(sinx)’
cosx
(cosx)’
-sinx
(tgx)’
1/cos^2 x
(arctgx)’
1/(x^2 +1)
(arcsinx)’
1/√1-X^2
(a^x)’
a^x lna
(sin(1/x))’
-cos(1/x)/x^2
lebo
von(dnu)’*dnu’
(f(g))’
f’(g)*g’
(f*g)’
f’g+fg’
(f/g)’
(f’g - fg’)/g^2
(f+g)’
f’+g’
(sin(3x))’
cos3x*3
∫sin(x)
-cos(x)
∫3^x lnx
3^x
∫a^x lna
a^x
1 =
sin^2x+cos^2x
cos^2x=
1-sin^2x
sin^2x
1-cos^2x
tg=
sin/cos
ctg=
cos/sin
sec=
1/sin
cosec=
1/cos
sin2x=
2sinx*cosx
cos2x=
cos^2x-sin^2x
sin(a+-b)=
sina cosb +- cosa sinb
Znamienko vstrede ostava
cos(a+-b)=.
cosa cosb -+ sina sinb
pozor! znamiekno v strede sa bim bam bum meni sup hop a je to inak naopak
podielove kriterium
lim Un+1 / Un
q > 1 Divergentna
q < 1 Konvergentna
q = 1 na picu
mocninove kriterium
lim nroot(Un)
Integracne kriterium
Int{1-inf}(Un dn)
ked existuje: konverguje
neabsolutna konvergencia
musi platit minimalne:
lim Un = 0
iterujuca rada
iterujuca rada absolutne konverguje ked plati lim(|Un|) = 0
ale stale moze byt neabsolutne konvergujuca ked sa nerovna 0
ln(e)
1
ln(1/e)
-1
∫sin(x/2)
-2cos(x/2)
∫e^2x
1/2 e^2x
