Derivatives

Question 1

arctan(0)

Answer 1

0

Question 2

arctan(1)

Answer 2

pi/4

Question 3

(e^x)’

Answer 3

e^x

Question 4

(x^a)’

Answer 4

ax^a-1

Question 5

(lnx)’

Answer 5

1/x

Question 6

(sinx)’

Answer 6

cosx

Question 7

(cosx)’

Answer 7

-sinx

Question 8

(tgx)’

Answer 8

1/cos^2 x

Question 9

(arctgx)’

Answer 9

1/(x^2 +1)

Question 10

(arcsinx)’

Answer 10

1/√1-X^2

Question 11

(a^x)’

Answer 11

a^x lna

Question 12

(sin(1/x))’

Answer 12

-cos(1/x)/x^2

lebo

von(dnu)’*dnu’

Question 13

(f(g))’

Answer 13

f’(g)*g’

Question 14

(f*g)’

Answer 14

f’g+fg’

Question 15

(f/g)’

Answer 15

(f’g - fg’)/g^2

Question 16

(f+g)’

Answer 16

f’+g’

Question 17

(sin(3x))’

Answer 17

cos3x*3

Question 18

∫sin(x)

Answer 18

-cos(x)

Question 19

∫3^x lnx

Answer 19

3^x

Question 20

∫a^x lna

Answer 20

a^x

Question 21

1 =

Answer 21

sin^2x+cos^2x

Question 22

cos^2x=

Answer 22

1-sin^2x

Question 23

sin^2x

Answer 23

1-cos^2x

Question 24

tg=

Answer 24

sin/cos

Question 25

ctg=

Answer 25

cos/sin

Question 26

sec=

Answer 26

1/sin

Question 27

cosec=

Answer 27

1/cos

Question 28

sin2x=

Answer 28

2sinx*cosx

Question 29

cos2x=

Answer 29

cos^2x-sin^2x

Question 30

sin(a+-b)=

Answer 30

sina cosb +- cosa sinb

Znamienko vstrede ostava

Question 31

cos(a+-b)=.

Answer 31

cosa cosb -+ sina sinb

pozor! znamiekno v strede sa bim bam bum meni sup hop a je to inak naopak

Question 32

podielove kriterium

Answer 32

lim Un+1 / Un

q > 1 Divergentna
q < 1 Konvergentna
q = 1 na picu

Question 33

mocninove kriterium

Answer 33

lim nroot(Un)

Question 34

Integracne kriterium

Answer 34

Int{1-inf}(Un dn)

ked existuje: konverguje

Question 35

neabsolutna konvergencia

Answer 35

musi platit minimalne:

lim Un = 0

Question 36

iterujuca rada

Answer 36

iterujuca rada absolutne konverguje ked plati lim(|Un|) = 0

ale stale moze byt neabsolutne konvergujuca ked sa nerovna 0

Question 37

ln(e)

Answer 37

1

Question 38

ln(1/e)

Answer 38

-1

Question 39

∫sin(x/2)

Answer 39

-2cos(x/2)

Question 40

∫e^2x

Answer 40

1/2 e^2x