Answers and Explanations 243
Answers
301–400
=
+
−
− −
+
=
+
+
x
x
x
x
x
x
x
(cos
)(cos ) (sin
)( sin )
(cos
)
cos
cos
s
1
1
1
2
2
i in
sin
(cos
)
cos
sin
(cos
)
2
2
2
1
1
1
x
x
x
x
x
x
−
+
=
−
+
+
x
( )
f '
335.
−
−
+
+
+
(
)
4
2
1
1
5
3
5
3
2
x
x
x
x
Apply the quotient rule to f x
x
x
x
( ) =
+
+
5
3
1
to get the following:
=
+
+
(
) −
+
(
)
+
+
(
)
= −
−
+
+
+
(
x
x
x x
x
x
x
x
x
x
x
( )
5
3
4
2
5
3
2
5
3
5
3
1 1
5
3
1
4
2
1
1 ) )
2
x
( )
f '
336.
− 19
16
The quotient rule gives you
f
g
x
g x f x f x g x
g x






=
−
[
]
( )
( ) ( ) ( ) ( )
( )
2
'
'
'
To find f
g





 ( )
' 4 , enter the numbers and solve:
f
g
g
f
f
g
g






=
−
[
]
=
− −
= −
( )
4
4
4
4
4
4
8
7
5 4
8
2
2
( ) ( ) ( ) ( )
( )
( )( ) ( )( )
1 19
16
'
'
'
337.
−
+
(
)
1
3
5
2
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
3
5
:
=
+
− +
+
=
−
+
x
x
x
x
(
)( ) (
)( )
(
)
(
)
3
5 1
2 3
3
5
1
3
5
2
2
x
( )
f '