LISTA 7
Pochodna i ró·
zniczka funkcji
c
0
= 0; c = const
(x )
0
= x
1
;
2 R
(
1
x
)
0
=
1
x
2
; x 2 R n f0g
(
p
x)
0
=
1
2
p
x
; x 2 R
+
[ f0g
(e
x
)
0
= e
x
; x 2 R
(a
x
)
0
= a
x
ln a; a 2 R
+
; x 2 R
(ln x)
0
=
1
x
; x 2 R
+
(log
a
x)
0
=
1
x ln a
; a 2 R
+
n f1g; x 2 R
+
(sin x)
0
= cos x; x 2 R
(cos x)
0
=
sin x; x 2 R
(tg x)
0
=
1
cos
2
x
; x 6=
2
+ k ; k 2 Z
(ctg x)
0
=
1
sin
2
x
; x 6= k ; k 2 Z
(arcsin x)
0
=
1
p
1
x
2
; x 2 ( 1; 1)
(arccos x)
0
=
1
p
1
x
2
; x 2 ( 1; 1)
(arctg x)
0
=
1
1 + x
2
; x 2 R
(arcctg x)
0
=
1
1 + x
2
; x 2 R