I differential calculations – Casio FX-9750GII User Manual
Page 62
2-24
I Differential Calculations
[OPTN]-[CALC]-[
d
/
dx
]
To perform differential calculations, first display the function analysis menu, and then input the
values using the syntax below.
*(CALC)* (
d
/
dx
)
f
(
x
)
a
tol
* fx-7400G
II
:
(CALC)
(
a
: point for which you want to determine the derivative,
tol
: tolerance)
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.
Example To determine the derivative at point
x
= 3 for the function
y
=
x
3
+ 4
x
2
+
x
– 6, with a tolerance of “
tol
” = 1
E
– 5
Input the function
f
(
x
).
*(CALC)* (
d
/
dx
)
T,B CTV T E
* fx-7400G
II
:
(CALC)
Input point
x
=
a
for which you want to determine the derivative.
B
Input the tolerance value.
@$ DU
Using Differential Calculation in a Graph Function
• Omitting the tolerance (
tol
) value when using the differential command inside of a graph
function simplifies the calculation for drawing the graph. In such a case, precision is
sacrificed for the sake of faster drawing. The tolerance value is specified, the graph is drawn
with the same precision obtained when you normally perform a differential calculation.
• You can also omit input of the derivative point by using the following format for the differential
graph: Y2=
d
/
dx
(Y1). In this case, the value of the X variable is used as the derivative point.
Differential Calculation Precautions
• In the function
f
(
x
), only X can be used as a variable in expressions. Other variables
(A through Z excluding X,
r
,
Ƨ
) are treated as constants, and the value currently assigned to
that variable is applied during the calculation.
• Input of the tolerance (
tol
) value and the closing parenthesis can be omitted. If you omit
tolerance (
tol
) value, the calculator automatically uses a value for
tol
as 1
E
–10.
• Specify a tolerance (
tol
) value of 1
E
–14 or greater. An error (Time Out) occurs whenever no
solution that satisfies the tolerance value can be obtained.
• Pressing
during calculation of a differential (while the cursor is not shown on the display)
interrupts the calculation.
d/dx ( f (x) a)
f (a)
dx
d
d/dx ( f (x) a)
f (a)
dx
d
f (a +
Ax) – f (a)
f (a) = lim –––––––––––––
Ax
Ax0
'
f (a +
Ax) – f (a)
f (a) = lim –––––––––––––
Ax
Ax0
'
f (a +
Ax) – f (a)
f (a) –––––––––––––
Ax
'
f (a +
Ax) – f (a)
f (a) –––––––––––––
Ax
'