Математический анализ I. Фомин В.И. - 114 стр.

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182
2
1 1
x
x
′
= −
2.
( ) ln
x x
a a a
′
=
( )
x x
e e
′
=
3.
(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
′
=
−
2
1 1
u
u
u
′
′
= − ⋅
2.
( ) ln
u u
a a a u
′ ′
= ⋅ ⋅
( )
u u
e e u
′ ′
= ⋅
3.
1
(log )
ln
a
u u
u a
′ ′
= ⋅
1
(ln )
u u
u
′ ′
= ⋅
4.
(sin ) cos
u u u
′ ′
= ⋅
5.
(cos ) sin
u u u
′ ′
= − ⋅
6.
2
1
(tg )
cos
u u
u
′ ′
= ⋅
7.
2
1
(ctg )
sin
u u
u
′ ′
= − ⋅
8.
2
1
(arcsin )
1
u u
u
′ ′
= ⋅
−
Продолжение прил. 3
( )
y f x
=
( ( ))
y f u x
=
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
′
=
9.
2
1
(arccos )
1
u u
u
′ ′
= − ⋅
−
10.
2
1
(arctg )
1
u u
u
′ ′
= ⋅
+
11.
2
1
(arcctg )
1
u u
u
′ ′
= − ⋅
+
12.
(sh ) ch
u u u
′ ′
= ⋅
13.
(ch ) sh
u u u
′ ′
= ⋅

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