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
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