Casio fx-9750G PLUS - Manual (Page 83)

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