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formule de derivare

formule de derivare

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formule de derivare
formule de derivare

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01/27/2013

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Reguli de derivare
1.

( )
f
=
αα
;2.

( )
'''
g f g f
±=±
;3.

===
     
n f n f
1''1
;4.

( )
gg f g f
'''
+=
;5.

== =
          
nn f  f  f  f n f
1'21'1
KK
;6.

2'''
g f gg f  g f
=
     
;7.

2''1
ggg
=
     
;8.

( )
( )
( )
'''
uu f u f
=
;9.

( )( )
( )
( )( ) ( )
''''
vvuvu f vu f
=
.10.

         
=
1'1'1
f  f  f
sau
              
=
0'10'1
x f  y f
, unde
    
=
00
x f  y
.

- 2 -
Tabel de derivare al functiilor elementare
Nr. Functia Derivata Domeniul de derivabilitate1
c
(constanta) 0
R
x

2
x
1
R
x

3
x

x x

0
x

4
n
x
,
N
n

1
n
nx

R
x

5
x
,
R

1
rx

( )
,0
x

6
x

x
21
( )
,0
x

7
n
x
,
N
n

n n
xn
1
1

( )
,0
x
daca
n
este par
0
x
daca
n
este impar
8
x
ln

x
1

( )
,0
x

9
x
ln

x
1

0
x

10
x
a
log
a x
ln1

( )
,0
x

11
x
e

x
e

R
x

12
x
a
,
1,0
>
aa

aa
x
ln

R
x

13
x
sin

x
cos

R
x

14
x
cos

x
sin

R
x

15
x
t
x x
22
tg1cos1
+=

ππ
x
+
2
,
Z

16
x
ctg
( )
x x
22
ctg1sin1
+=

π
x
,
Z

17
x
arcsin

2
11
x

( )
1,1
x

18
x
arccos

2
11
x

( )
1,1
x

19
x
arct
2
11
x
+

R
x

20
x
arcctg
2
11
x
+

R
x

21
2ch
x x
ee x
+=
2sh
x x
ee x
=

R
x

22
2sh
x x
ee x
=
2ch
x x
ee x
+=

R
x
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