Izvodi Formule

IZVODI Tabli ni izvodi:

(sin x )' = cos x (cos x )' = − sin x

(C )' = 0 ( x )' = 1

(x )' = nx n

n −1

1 1  ' = − 2 x x n  1   n ' = − n +1 x x  1 x '= 2 x x e '= ex

( )

( ) (a )' = a x

x

ln a

(ln x )' = 1 x

(log a x )' =

1 x ln a

(arcsec x )' =

(tan x )' =

1 cos 2 x (cot x )' = − 12 sin x (arcsin x )' = 1 2 1− x (arccos x )' = − 1 2 1− x (arctan x )' = 1 2 1+ x (arccot x )' = − 1 2 1+ x (sec x )' = sin2x cos x (cosec x )' = − cos2 x sin x

x x2 −1 (arccosec x )' = − 12 x x −1 (sinh x )' = cosh x (cosh x )' = sinh x

(tanh x )' =

1 cosh 2 x (coth x )' = − 1 2 sinh x (Areasinh x )' = 1 2 1+ x (Areacosh x )' = 21 x −1 (Areatanh x )' = 1 2 1− x (Areacoth x )' = 1 2 1− x

(au + bv )' = au'+bv' (u ⋅ v )' = u'⋅v + u ⋅ v'

Izvodi nekih slo enijih funkcija:

1

a, b = const u, v su proizvoljne funkcije

 u  u'⋅v − u ⋅ v'  ' = v2 v

LIMESI n

n

1  1 +  = e lim n n →∞  sin x =1 lim x x →0

x  x 1 ±  = e lim n n→ ∞  xn = 0 ; za a > 1 lim x n →∞ a

ex =∞ lim n x →∞ x

lim a x→0

x

= 1 ; za a > 0