ΠΙΝΑΚΑΣ ΑΝΑΚΕΦΑΛΑΙΩΣΗΣ
Κανόνες παραγώγισης
(f(x)±g(x))'=f'(x)±g'(x)
(c · f(x))' = c · f '(x)
(f(x) · g(x))' = f ' (x) · g(x) + f(x) · g' (x)
⎛ 1 ⎞′
g′(x)
⎜
⎟ =−
2
⎝ g(x) ⎠
[g(x)]
⎛ f (x) ⎞′ f ′(x)g(x) − f (x)g′(x)
⎜
⎟ =
2
⎝ g(x) ⎠
[ g(x)]
(g o f)'(x) = g'(f(x)) f '(x)
Παράγωγοι βασικών συναρτήσεων
Παράγωγοι σύνθετων συναρτήσεων
(c)' = 0
(x)' = 1
(xν)'=νxν-1,
( x )′ = 2 1 x
v ∈ N*
(για κάθε x > 0)
([f(x)]v)'=v [f(x)]v-1.f '(x)
(
)
′
f (x) =
1
f ′(x) f(x)>0
2 f (x)
(ηµx)' = συνx
(ηµf(x))' = συνf(x)·f '(x)
(συνx)' = - ηµx
(συνf(x))' = - ηµf(x)· f '(x)
1
f '(x), f(x) > 0
f (x)
(lnx)' =
1
, x>0
x
(lnf(x))' =
(ln|x|)'=
1
x
( ln |f(x)| )' =
(εφx)' =
1
συν 2 x
( εφf (x) )′ =
1
⋅ f ′(x)
συν 2 f (x)
( σφf (x) )′ = −
1
⋅ f ′(x)
ηµ f (x)
(ex)' = ex
( e )′ = e
⋅ f ′(x)
(αx)' =αx · lnα
( α )′ = α
(σφx)' = −
1
ηµ 2 x
1
f '(x)
f (x)
( x t )' = τ ·x t - 1 ,
f (x )
f (x )
t ∈ R, x > 0
f (x )
2
f (x )
⋅ ln α ⋅ f ′(x)
([f (x)] )′ = t [f (x)]
t
t −1
⋅ f ′(x)