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Differential Calculations Chapter 3
• To perform differential calculations, first display the Option Menu, and then input
the values shown in the formula below.
K2(CALC)[
1(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.
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
d
d/dx ( f (x), a, !x) $ ––– f (a)
dx
Increase/decrease of
x
Point for which you want to determine the derivative
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