Tabelul derivatelor functiilor elementare si a celor compuse

Functia

Derivata

Domeniul de

derivabilitate

Functia  compusa

Derivata

c

R

x

R

u

u'

xⁿ (n є N^*)

nx^n-1

R

uⁿ (n є N^*)

nu ^n-1u'

x (α є R)

αx^α-1

D_f'

u^α (α є R , u>0)

a ∙ u^α-1∙u'

-

R^*

(u 0)

-

(u > 0)

e^x

e^x

R

e^u

e^u ∙ u'

a^x , 0<a1

a^x ln a

R

a^u (0<a1)

a^x ∙ u' ∙ ln a

ln x

ln u (u > 0)

log_a x , 0<a1

log_a u (u > 0)

sin x

cos x

R

sin u

cos u ∙ u'

cos x

sin x

R

cos u

-sin x ∙ u'

tg x

cos x 0

tg u (cos u 0)

ctg x

-

sin x 0

ctg u (sin u 0)

-

arcsin x

arcsin u (|u| ≤ 1)

arccos x

-

arccos u (|u| ≤ 1)

-

arctg x

R

arctg u

arcctg x

-

R

arcctg u

-

sh x =

= ch x

R

sh u

ch u ∙ u'

ch x =

= sh x

R

ch u

sh u ∙ u'