Differential Calculations - Casio FX-9750G PLUS User's Manual & Technical Reference

3-2 Differential Calculations

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