Tabel Cu Derivatele Element Are

Tabel cu derivatele elementare

Funcţia c constant x n x (n ∈N *) xa( a ∈ R ) 1 x x

Derivata 0 1 nxn-1 axa-1 −

1 x2 1

arc sin x

2 x ex x a ln a 1 x 1 x ln a cos x - sin x 1 cos 2 x 1 − sin 2 x 1

arc cos x

1− x 1

x

e a , (0 < a ≠ 1) ln x x

loga x, 0 < a ≠ 1 sin x cos x tg x ctg x

arc tg x Arc ctg x

1− x 1 1+ x2 1 − 1+ x2

Funcţia compusă

Derivata

U Un( n ∈ N * )

U’ n ⋅ u n -1 ⋅ u' a ⋅ u a -1 ⋅ u'

Ua( a ∈ R, u > 0 ) 1 (u ≠ 0) u u (u > 0)

−

u' u2 U

arc sin U ( U ≤ 1 )

2 U eu = U’ a u ⋅ u' ⋅ ln a U' U U' U ln a cos U ⋅ U' - sin U – U’ U' − cos 2 U U' - 2 sin U U'

arc cos U ( U ≤ 1 )

1- U2 U'

u

e a (0 < a ≠ 1) ln U (U > 0) u

logaU(U > 0) sin U cos U tg U (U ≠ 0) ctg U (cos Ux ≠ 0)

Arc tg U Arc ctg U

−

1- U2 U' 1- U2 U' − 1+ U2