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FORMULE DI DERIVAZIO$E ( Indicheremo la derivata di una funzione con
Df x( ),
f' x( ))
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( ) ( ) ( ) ( )
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[ ] [ ] [ ] ( )
( ) ( )
( )
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)) (
) ( ) ' ( ) ( ln ) ( ' ) ( ) ( ) ( ) ( ( )
2(
) ( ' ) ( ) ( ) ( ' ) (
) (
) ( ' ) ( ) ( ) ( ' ) ( ) ( )
( ' ) ( ' ) ( ) ( ) ln
) ( ( ) ' (
) ) ( ( ) ' log (
) (
) ( ) ' ( log )
( ) ( ) ' ( ln ) 1
( ) ( ) '
(
2 ) ( ) ' ( )
( 1 ' )
( )
( 1 ' )
(
' )
( )
) 2 ( 1 ( ) 1 ( )
( ' )
(
) ( sen ) 1 ( cos ) ( ' )
( cos )
( cos ) 1 ( sen ) ( ' )
( sen
1 2 )
senh(
cosh )
cosh(
senh
) ) 2 ( 1 ( ) ( ' ) ( )
( sen ) ( ' ) ( cos )
( cos ) ( ' ) ( sen
) 2( 1
) ( ) '
( arctg )
2( 1
) ( ) '
( arccos )
2( 1
) ( ) '
( arcsen
1 2 arctg 1 1 2
arccos 1 1 2
arcsen 1
2 ) 1 ( sen
cos cos
sen
ln 1 log
) ( 1 log
) ln(
1 1 2
1 2
2 1 1
1 1 1
0
x f
x x f g x f x x g
x g x f
x g Df x
g
x g x f x g x f x g
x D f
x g x f x g x f x g x f D x
g x f x g x f D x a
af x x f
Daf
x ef x x f
Def ae
x f
x x f
a f D x
f x x f
f D
n n
x f n
x n f x f
D
x f
x x f
f D x
n f x kf n n x f Dk x
n f x f n n x Df
x f k x f Dk x
f tg x
n f tg x f n x n f Dtg
x f x n f
x f n x n f D x
f x n f
x f n x n f D
x tgh x
Dtgh x
x D x
x D
x f tg x
f x f Dtg x
f x f x f D x
f x f x f D
x f
x x f
f D x
f x x f
f D
x f
x x f
f D
x x D x
x D
x x
D
x tg Dtgx
x x
D x
x D
x a x a x Da
x e De ae
x a x D x
x D
n nx n nx D x
x D x
k x Dk x x
D
xn n nk n Dkx
x n n Dx k
Dkx Dx
Dk
⋅ +
⋅
⋅
− =
=
+
=
⋅
±
=
±
⋅
⋅
=
⋅
=
⋅
=
− =
⋅
=
=
− ⋅
⋅
=
⋅
− ⋅
⋅
=
⋅
=
⋅ +
− ⋅
⋅
⋅
=
− ⋅
⋅
⋅
−
=
− ⋅
⋅
⋅
=
−
=
=
=
+
⋅
=
⋅
−
=
⋅
=
= +
−
= −
−
=
+
=
−
= −
−
=
+
=
−
=
=
⋅
=
=
⋅
=
=
= −
=
−
=
−
=
⋅ −
− =
⋅
=
=
=
=
