Derivate 1w4vj

f ' ( a ) = lim x→ a

f ( x) − f ( a) x−a

(e ) = e x '

x

c' = 0

(2 ) = 2

x' = 1

( sin x ) ' = cos x

x '

(x ) = n⋅ x n '

n −1

x

⋅ ln 2

( cos x ) ' = − sin x 1 cos 2 x

(x ) = 2⋅ x

( tgx ) ' =

( x ) = 3⋅ x

( ctgx ) ' = −

2 '

3 '

( x) =

2

1

'

n

n ⋅ n x n −1

'

1 f'   = − 2 f f

( x ) = 2 ⋅1 x

(f

( x) =

( f ⋅ g)' =

'

1

'

3

3

3 x

(x ) = α ⋅ x α '

2

α −1

1 sin 2 x

+ g) = f ' + g' '

f ' ⋅ g + f ⋅ g'

Consecinte:

'

1 1   =− 2 x  x

( log a x ) ' =

1 x ⋅ ln a

( ln x ) ' = 1 x

( lg x ) ' =

1 x ⋅ ln 10

1 log 2 x = x ⋅ ln 2

(a ) = a x '

x

⋅ ln a

Daca avem o functie constanta sau o functie de derivat:

(c ⋅ f )' = c ⋅ f ' (− f )' = − f ' (f

− g) = f ' − g' '

'

f f ' ⋅ g − f ⋅ g'   = g2 g