Part II: The Answers
246
Answers
301–400
345.
1
2
cos
sin
x
x
+
(
)
Apply the quotient rule to f x
x
x
x
( )
sin
cos
sin
=
+
to get the following:
=
+
−
−
+
+
=
x
x
x
x
x
x
x
x
x
(cos
sin )(cos ) sin ( sin
cos )
(cos
sin )
cos
2
2
+ +
+
−
+
=
+
cos sin
sin
cos sin
(cos
sin )
(cos
sin )
x
x
x
x
x
x
x
x
x
2
2
2
1
x
( )
f '
346.
6
5
3 1
4 3
1 3
2
x
x
x
+
+
(
)
Apply the quotient rule to f x
x
x
( ) = +
2
3
1
:
=
+
(
) − ( )
+
(
)
=
+
+
(
)
=
+
−
x
x x
x
x
x
x
x
x
( )
1
2
1
3
1
2
5
3
1
6
5
1 3
2
23
1 3
2
4 3
1 3
2
x x
x
4 3
1 3
2
3 1+
(
)
x
( )
f '
347.
−
+
(
)
1
2
1
2
x x
Apply the quotient rule to f x
x
x
( ) =
+
+
2
1
to get
=
+
(
) ( ) − +
(
) ( )
+
(
)
=
−
+
(
)
=
−
−
−
−
x
x
x
x
x
x
x
x
1 1
2
2 1
2
1
1
2
1
1
2
1 2
1 2
2
1 2
2
x x +
(
)
1
2
x
( )
f '