3-22
k
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.
K
4
(CALC)
2
(
d
/
dx
)
f
(
x
)
,
a
,
tol
!
/
( ) )
(
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
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.
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
).
A
K
4
(CALC)
2
(
d
/
dx
)
a5
(U-Z)
4
(X)
!
a
(CATALOG)
a6
(SYBL)
4
(
9
)
c
~
c
(^)
w
d+e
a5
(U-Z)
4
(X)
x
+
4
(X)
-g,
Input point
x
=
a
for which you want to determine the derivative.
d,
Input the tolerance value.
b
!
a
(CATALOG)
a1
(A-E)
5
(E)
c
~
c
(EXP)
w
-f
!
/
( ) )
w
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
A
during calculation of a differential (while the cursor is not shown on the display)
interrupts the calculation.
• Inaccurate results and errors can be caused by the following:
- discontinuous points in
x
values
- extreme changes in
x
values
- inclusion of the local maximum point and local minimum point in
x
values
d
/
dx
(
f
(
x
)
,
a
)
⇒
f
(
a
)
dx
d
d
/
dx
(
f
(
x
)
,
a
)
⇒
f
(
a
)
dx
d
f
(
a
+
A
x
) –
f
(
a
)
f
(
a
) = lim
–––––––––––––
A
x
A
x
→
0
'
f
(
a
+
A
x
) –
f
(
a
)
f
(
a
) = lim
–––––––––––––
A
x
A
x
→
0
'
f
(
a
+
A
x
) –
f
(
a
)
f
(
a
)
–––––––––––––
A
x
'
f
(
a
+
A
x
) –
f
(
a
)
f
(
a
)
–––––––––––––
A
x
'
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