Answers and Explanations 245
Answers
301–400
342.
8
8
4
4
2
2
2
x
x
x
x
x
x
x
x
x
x
sin
c os
cos
s in
sin
cos
+
−
+
+
(
)
Apply the quotient rule to f x
x
x
x
( ) sin
cos
=
+
4
2
:
=
+
− ( )
−
+
=
+
x
x
x
x
x
x
x
x
x
x
(sin
cos )( )
(cos
sin )
(sin
cos )
sin
8
4
8
2
2
8 8
4
4
2
2
2
x
x
x
x
x
x
x
x
cos
c os
sin
(sin
cos )
−
+
+
x
( )
f '
343.
− 38
49
The quotient rule says that
f
g
x
g x f x f x g x
g x






=
−
[
]
( )
( ) ( ) ( ) ( )
( )
2
'
'
'
To find f
g






′ ( )
5 , enter the numbers and solve:
f
g
g f
f
g
g






=
−
[
]
=
−
− − −
−
( )
( ) ( ) ( ) ( )
( )
( )( ) ( )( )
(
5
5
5
5
5
5
7 2
4
6
2
7 7
38
49
2
)
= −
'
'
'
344.
4
3
2 1
3 2
1 2
2
x
x
x
+
+
(
)
Recall that the quotient rule states
d
dx
f x
g x
g x f x f x g x
g x
( )
( )
( ) ( ) ( ) ( )
( )





 =
−
[
]
2
'
'
Apply the quotient rule to f x
x
x
( ) = +
2
1
to get
=
+
(
) − ( )
+
(
)
=
+
−
+
(
)
−
x
x x
x
x
x
x
x
x
( )
1
2
1
2
1
2
2
1
2
1
1 2
2
1 2
1 2
2
3 2
3 2
1 2
2
= =
+
+
(
)
=
+
+
(
)
2
3
2
1
4
3
2 1
3 2
1 2
2
3 2
1 2
2
x
x
x
x
x
x
x
( )
f '