Part II: The Answers
248
Answers
301–400
351.
−
( )
+ ( )
( )
 
 
g x
x g x
x
g x
sin
'
cos
2
Applying the quotient rule to f x
x
g x
( ) cos
( )
=
gives you
=
−
[
]−
[
]
= −
+
g x
x
x g x
g x
g x
x g x
x
g
( ) sin
(cos ) ( )
( )
( )sin
( )cos
(
2
x x )
[
]
2
x
( )
f '
'
'
352.
100 2
3
3
2
99
x
x
x
+
(
) +
(
)
Recall that the chain rule states
d
dx
f g x
f g x g x
( )
( ) ( )
(
)= (
)
'
'
Applying the chain rule to f x
x
x
( ) =
+
(
)
2
100
3
gives you
f x
x
x
x
x
x
x
( ) =
+
(
)
+
(
)
=
+
(
) +
(
)
100
3
2
3
100 2
3
3
2
99
2
99
'
353.
4 cos(4x)
Apply the chain rule to f
 
(x) = sin(4x):
f x
x
x
'
c os
cos
( ) =
( )
 
  ( )
=
( )
4
4
4
4
354.
sec tan
sec
x
x
x
3 1
2 3
+
(
)
Rewrite the function using exponential notation:
f x
x
x
( )
sec
s ec
= +
= +
(
)
1
1
3
1 3
Then apply the chain rule:
x
x
x
x
x
x
sec
s ec tan
sec tan
sec
( ) =
+
(
) (
)
=
+
(
)
−
1
3
1
3 1
2 3
2 3
x
f '
355.
−
−
−
(
)
5 2 1
2
6
(
)
x
x x
Rewrite the function as
f x
x x
x x
( ) =
−
(
)
=
−
(
)
−
1
2
5
2
5