Differential Calculations - Casio fx9750G User Manual

3-3 Differential Calculations

P.64
The differentiation for this type of calculation is defined as:
In this definition, infinitesimal is replaced by a sufficiently small ∆
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, ∆
difference.To calculate derivatives, the unit takes the average between the value of
∆
• 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)
)
d/dx ( f (x), a, ∆x) ⇒ ––– f (a)
f (a + ∆x) – f (a)
f '(a) = lim –––––––––– –––
∆x→0
f (a + ∆x) – f (a)
–––––––––– –––
f '(a)
a
and point
are as follows:
f (a + ∆x) – f (a)
–––––––––– ––– = ––– , –––––––––– ––– = –––
∆x
is called the forward difference, while ∇
y x
/∆
and ∇
y x y x
/∆ /∇ , thereby providing higher precision for derivatives.
, ,∆ )
a x
Increase/decrease of
Point for which you want to determine the derivative
d
dx
∆x
∆x
∆
a + x
, and of point
∆ f (a) – f (a – ∆x)
y
∆x ∆x
x
x
, with the value in
∆
a a – x
and point in function
∇
y
∇x
y x
/∇ is the backward
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