Answers and Explanations 247
Answers
301–400
348.
(sec )( sec
tan )
sec
x
x
x
x
1
1
2
+
+
+
(
)
Apply the quotient rule to f x
x
x
( ) tan
sec
=
−
+
1
1
as follows:
=
+
−
−
+
=
+
x
x
x
x
x
x
x
(sec
)sec
(tan
)(sec tan )
(sec
)
sec
sec
1
1
1
2
2
3
2 x x
x
x
x
x
x
x
x
x
x
−
+
+
=
+
−
+
tan sec
sec tan
(sec
)
(sec )(sec
sec
tan
tan
2
2
2
2
1
x x
x
x
x
x
x
)
(sec
)
(sec )( sec
tan )
(sec
)
+
=
+
+
+
1
1
1
2
2
x
( )
f '
Note that the identity sec
2 
x – tan
2 
x = 1 was used to simplify the final expression.
349.
8
4
2
2
x
x +
(
)
First multiply the numerator and denominator by x:
f x
x
x x
x
x
( ) =
+
=
+
4
4
2
2
Then use the quotient rule to find the derivative:
=
+
(
) −
+
(
)
=
+
(
)
x
x x
x
x
x
x
( )
( )
2
2
2
2
2
2
4 2
2
4
8
4
x
( )
f '
350.
xg x
g x
x
' ( )− ( )
3
4
Applying the quotient rule to f x
g x
x
( )
( )
=
3
, followed by factoring and simplifying, gives
you the following:
=
−




( )
=
−
 
 
=
x g x g x
x
x
x xg x
g x
x
xg x
( ) ( )
( )
( )
( )
2
3
3
2
2
6
3
3
− − 3
4
g x
x
( )
x
( )
f '
'
'
'