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Приложение 3
ТАБЛИЦА ПРОИЗВОДНЫХ ОСНОВНЫХ ЭЛЕМЕНТАРНЫХ
ФУНКЦИЙ
()yfx= (())yfux
=
1.
1
()
x
x
αα−
′
=α
()
1
2
x
x
′
=
2
11
x
x
′
=−
2.
() ln
xx
aaa
′
=
()
xx
ee
′
=
3.
1
(log )
ln
a
x
x
a
′
=
1
(ln )x
x
′
=
4.
(sin ) cos
x
x
′
=
5.
(cos ) sin
x
x
′
=
−
6.
2
1
(tg )
cos
x
x
′
=
7.
2
1
(ctg )
sin
x
x
′
=−
8.
2
1
(arcsin )
1
x
x
′
=
−
1.
1
()uuu
αα−
′
′
=
α⋅
()
1
2
uu
u
′
′
=
⋅
2
11
u
u
u
′
′
=
−⋅
2.
() ln
uu
aaau
′
′
=
⋅⋅
()
uu
eeu
′
′
=
⋅
3.
1
(log )
ln
a
uu
ua
′
′
=
⋅
1
(ln )uu
u
′
′
=
⋅
4.
(sin ) cosuuu
′
′
=
⋅
5.
(cos ) sinuuu
′
′
=
−⋅
6.
2
1
(tg )
cos
uu
u
′
′
=
⋅
7.
2
1
(ctg )
sin
uu
u
′
′
=
−⋅
8.
2
1
(arcsin )
1
uu
u
′
′
=
⋅
−
9.
2
1
(arccos )
1
x
x
′
=−
−
10.
2
1
(arctg )
1
x
x
′
=
+
11.
2
1
(arcctg )
1
x
x
′
=−
+
12.
(sh ) ch
x
x
′
=
13.
(ch ) sh
x
x
′
=
14.
2
1
(th )
ch
x
x
′
=
15.
2
1
(cth )
sh
x
x
′
=−
9.
2
1
(arccos )
1
uu
u
′
′
=
−⋅
−
10.
2
1
(arctg )
1
uu
u
′
′
=
⋅
+
11.
2
1
(arcctg )
1
uu
u
′
′
=
−⋅
+
12.
(sh ) chuuu
′
′
=
⋅
13.
(ch ) shuuu
′
′
=
⋅
14.
2
1
(th )
ch
uu
u
′
′
=
⋅
15.
2
1
(cth )
sh
uu
u
′
′
=
−⋅
