21
‫טבלת הנגזרות‬
x′ = 1
(u ⋅ v)′ = u ′v + uv ′
′
⎛ u ⎞ u ′v − uv ′
⎜ ⎟ =
v2
⎝v⎠
2
4
(c ) ′ = 0
(‫ קבוע‬- c )
(u + v + w)′ = u ′ + v′ + w′
6
(c ⋅ u )′ = cu ′
8
(u α )′ = α ⋅ u α −1u ′
10
( x α )′ = α ⋅ x α −1
12
( x )′ =
14
(l x ) ′ = l x
1
2 u
⋅ u′
(l u ) ′ = l u ⋅ u ′
(a u )′ = a u ln a ⋅ u ′
16
5
′
⎛ u ⎞ u′
⎜ ⎟ =
c
⎝c⎠
7
‫ מספר ממשי‬- α
1
l ≈ 2 .7 K
(a x )′ = a x ⋅ ln a
1
⋅ u′
u
18
(ln x)′ =
(sin x)′ = cos x
20
(log a u )′ =
(cos x)′ = − sin x
22
1
cos 2 x
1
(cot x)′ = − 2
sin x
1
(arcsin u )′ =
⋅ u′
1− u2
u′
(arctan u )′ =
1+ u2
24
( f [g ( x)])′
32
(tan x)′ =
= f ′[g ( x)] ⋅ g ′( x)
x ′y =
1
y ′x
26
28
30
34
13
15
(‫ קבוע‬-a )
1
x
17
1
⋅ u′
u ln a
19
(sin u )′ = cos u ⋅ u ′
(cos u )′ = − sin u ⋅ u ′
(tan u )′ =
9
11
2 x
a>1
(ln u )′ =
3
( x ‫ פונקציות של‬- w , v, u)
′
c
⎛c⎞
⎜ ⎟ = − 2 ⋅ v′
v
⎝v⎠
( u )′ =
1
1
⋅ u′
cos 2 u
1
⋅ u′
sin 2 u
1
(arccos u )′ = −
⋅ u′
2
1− u
u′
(arc cot u )′ = −
1+ u2
(cot u )′ = −
y ′′ = ( y ′)′
21
23
25
27
29
31
33