Casio fx-9750G Differential/Quadratic Differential, Integration, Value - Manual (Page 5)

67
3-3 Differential Calculations
• 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 ,
∆
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.
P.64
Increase/decrease of x
Point for which you want to determine the derivative
d
d/dx ( f (x), a,
∆
x)
⇒
––– f (a)
dx
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