2 differential calculations – Casio fx-9750G PLUS User Manual
Page 83
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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 + Ax) – f (a)
f
'(a) = lim
–––––––––––––
A
x
A
x
→0
f
(a + Ax) – f (a)
A
y
f
(a) – f (a – Ax)
∇
y
––––––––––––– = ––– , ––––––––––––– = –––
A
x
A
x
A
x
∇x
f
(a + Ax) – 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, Ax)
⇒ ––– f (a)
dx
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