Casio fx-7400G PLUS, User Manual

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44
Chapter 3 Differential Calculations
• To perform differential calculations, first display the Option Menu, and then input
the values shown in the formula below.
K 2
(CALC)
[
1
(
d
/
dx
)
f ( x )
,
a
,
∆ x
)
The differentiation for this type of calculation is defined as:
In this definition, infinitesimal is replaced by a sufficiently small
∆ x
, with the value in
the neighborhood of
f ' ( a )
calculated as:
In order to provide the best precision possible, this unit employs central difference to
perform differential calculations. The following illustrates central difference.
The slopes of point
a
and point
a
+ ∆
x
, and of point
a
and point
a
– ∆
x
in function
y = f ( x )
are as follows:
In the above,
∆
y
/
∆
x
is called the forward difference, while
∇
y
/
∇
x
is the backward
difference.To calculate derivatives, the unit takes the average between the value of
∆ y
/
∆ x
and
∇ y
/
∇ x
, thereby providing higher precision for derivatives.
f ( a +
∆
x ) – f ( a )
f
'(
a
) = lim –––––––––––––
∆
x
∆
x
→
0
f
(
a
+
∆
x
) –
f
(
a
)
∆ y
f
(
a
) –
f
(
a
–
∆
x
)
∇ y
––––––––––––– = ––– , ––––––––––––– = –––
∆
x
∆
x
∆
x
∇
x
f ( a +
∆
x ) – f ( a )
f
'(
a
) –––––––––––––
∆
x
d
d / dx ( f ( x ), a ,
∆
x )
⇒
–––
f ( a )
dx
Increase/decrease of
x
Point for which you want to determine the derivative