Сборник задач по высшей математике. Часть II. Введение в математический анализ. Дифференциальное исчисление функции одного вещественного аргумента. Гиль Л.Б - 67 стр.

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66
Таблица 2.2.1
Производные основных элементарных функций
П р о с т ы е ф у н к ц и и С л о ж н ы е ф у н к ц и и
( )
1
1.
x x
α α
α
−
′
=
( )
1
1.
U U U
α α
α
−
′
′
= ⋅
( )
1
2.
2
x
x
′
=
( )
1
2.
2
U
′
′
= ⋅
2
1 1
3.
x x
′
= −
2
1 1
3.
U
U U
′
′
= − ⋅
( )
1
4. ln x
x
′
=
( )
1
4. ln
U U
U
′
′
= ⋅
( )
5. ln
x x
a a a
′
= ⋅
( )
5. ln
U U
a a a U
′
′
= ⋅ ⋅
( )
6.
x x
e e
′
=
( )
6.
U U
e e U
′
′
= ⋅
( )
7. sin cos
x x
′
=
( )
7.
sinU cosU U
′
′
= ⋅
( )
8. cos sin
x x
′
= −
( )
8.
cosU sinU U
′
′
= − ⋅
( )
2
1
9. tgx
cos x
′
=
( )
2
1
9.
tgU U
cos U
′
′
= ⋅
( )
2
1
10. ctgx
sin x
′
= −
( )
2
1
10.
ctgU U
sin U
′
′
= − ⋅
( )
2
1
11. sin
1
arc x
x
′
=
−
( )
2
1
11. sin
1
arc U U
U
′
′
= ⋅
−
( )
2
1
12. cos
1
arc x
x
′
= −
−
( )
2
1
12. cos
1
arc U U
U
′
′
= − ⋅
−
( )
2
1
13.
1
arctgx
x
′
=
+
( )
2
1
13.
1
arctgU U
U
′
′
= ⋅
+
( )
2
1
14.
1
arcctgx
x
′
= −
+
( )
2
1
14.
1
arcctgU U
U
′
′
= − ⋅
+
15.( )
shx chx
′
=
15.( )
shu chu u
′ ′
= ⋅
16.( )
chx shx
′
=
16.( )
chu shu u
′ ′
= ⋅
2
1
17.( )thx
ch x
′
=
2
1
17.( )
thu u
ch u
′ ′
=
( )
1
18. ln
V V V
U VU U U U V
−
′
′ ′
= ⋅ + ⋅

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