In terms of communication, information is expressed either as the content of a message or through direct or indirect observation. That which is perceived can be construed as a message in its own right, and in that sense, information is always conveyed as the content of a message.
Information can be encoded into various forms for transmission and interpretation (for example, information may be encoded into a sequence of signs, or transmitted via a signal). It can also be encrypted for safe storage and communication.
Answer:
F '( 1 ) = 84
Explanation:
We will differentiate
F
and wade our way slowly and methodically through finding the derivative of the right. First with the outermost function and chain rule:
F
(
x
)
=
f
(
x
f
(
x
f
(
x
)
)
)
F
'
(
x
)
=
f
'
(
x
f
(
x
f
(
x
)
)
)
(
d
d
x
x
f
(
x
f
(
x
)
)
)
Now applying the product rule:
F
'
(
x
)
=
f
'
(
x
f
(
x
f
(
x
)
)
)
[
f
(
x
f
(
x
)
)
+
x
(
d
d
x
f
(
x
f
(
x
)
)
)
]
Reapplying the chain rule:
F
'
(
x
)
=
f
'
(
x
f
(
x
f
(
x
)
)
)
[
f
(
x
f
(
x
)
)
+
x
(
f
'
(
x
f
(
x
)
)
+
(
d
d
x
x
f
(
x
)
)
)
]
F
'
(
x
)
=
f
'
(
x
f
(
x
f
(
x
)
)
)
[
f
(
x
f
(
x
)
)
+
x
f
'
(
x
f
(
x
)
)
+
x
(
d
d
x
x
f
(
x
)
)
]
Product rule once more:
F
'
(
x
)
=
f
'
(
x
f
(
x
f
(
x
)
)
)
[
f
(
x
f
(
x
)
)
+
x
f
'
(
x
f
(
x
)
)
+
x
(
f
(
x
)
+
x
f
'
(
x
)
)
]
We could simplify this a little more, but I'm dubious it would help. Evaluating at
x
=
1
:
F
'
(
1
)
=
f
'
(
f
(
f
(
1
)
)
)
[
f
(
f
(
1
)
)
+
f
'
(
f
(
1
)
)
+
1
(
f
(
1
)
+
f
'
(
1
)
)
]
F
'
(
1
)
=
f
'
(
f
(
2
)
)
[
f
(
2
)
+
f
'
(
2
)
+
2
+
4
]
F
'
(
1
)
=
f
'
(
3
)
(
3
+
5
+
2
+
4
)
F
'
(
1
)
=
6
(
14
)
F
'
(
1
)
=
84