Part II: The Answers
264
Answers
301–400
Then apply the chain rule to each term to get the derivative:
= +
( ) − −
−
( )
= +
+ −
e
e
e
e
e
e
e
e
x
x
x
x
x
x
x
x
1
1
1
1
1
1
( )
x
f '
398.
x
x
x
x
x
x
2
2
2
1
6 6 1 2 6
1
+
(
)(
) (
)
(
)
(ln ) + −
+
+
Apply the quotient rule to find the derivative of f x
x
x
x
( ) =
+
+
6
1
2
:
(
)(
) (
)
(
)
(
)(
x
x
x
x
x
x
x
x
=
+
+ −
+
+
=
+
+
2
2
2
2
1 6
6 1
6
2
1
1
6 6 1
(ln )
( )
(ln )
) ) (
)
(
)
−
+
+
2 6
1
2
2
x
x
x
x
f x
' ( )
399.
−
−
+
−
4
2
e e
e e
x
x
x
x
−
(
)
(
)
First rewrite the function:
f x
e e
e e
x
x
x
x
( ) =
+
=
+
−
−
−
4
4
1
(
)
Applying the chain rule gives you the derivative as follows:
(
) (
)
=
(
)
(
)
e e
e e
e e
e e
x
x
x
x
x
x
x
x
( )
= −
+
+
−
−
−
+
−
−
−
−
−
1
4
4
2
2
( )
x
f '
400.
8
2 8
2 1
2
x
x
x
x
x
+
+
( ) [
]
(
)
( ln ) cos
sin
cos
To find the derivative of f x
x
x
( ) cos
=
+
8
2 1 , apply the quotient rule while applying the chain
rule to the numerator:
=
(
)
(
)
(
)
=
( )
x
x
x
x
x
x
x
cos
( ln )( )
s in
cos
( ln
8
8 2
8
8
2
2
2
2
1
1
2
1
+
+
+
−
−
8 8
2
) cos
sin
cos
x
x
x
x
+
[
]
(
)
( )
x
f '