Casio CFX-9850G PLUS, User'S Manual & Technical Reference

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55
3-2 Differential Calculations
[OPTN]
-
[CALC]
-
[
d
/
dx
]
To perform differential calculations, first display the function analysis menu, and
then input the values shown in the formula below.
2
(
d
/
dx
)
f ( x )
,
a
, A
x
)
The differentiation for this type of calculation is defined as:
In this definition, infinitesimal is replaced by a sufficiently small
A
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.
A
A
A A
A
A A
The slopes of point
a
and point
a +
A
x
, and of point
a
and point
a –
A
x
in function
y = f ( x )
are as follows:
In the above,
A
y
/
A
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
A
y
/
A
x
and
∇
y
/
∇
x
, thereby providing higher precision for derivatives.
f ( a +
A
x ) – f ( a )
f
'(
a
) = lim –––––––––––––
A
x
A
x
→
0
f ( a +
A
x ) – f ( a )
A
y
f ( a ) – f ( a –
A
x )
∇ y
–––––––––––––
=
–––
,
–––––––––––––
=
–––
A
x
A
x
A
x
∇
x
f ( a +
A
x ) – f ( a )
f '( a )
–––––––––––––
A
x
Increase/decrease of
x
Point for which you want to determine the derivative
d
d / dx ( f ( x ), a ,
A
x )
⇒
–––
f ( a )
dx