User Manual

2-24
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.
K4(CALC) * 2( d / dx ) f ( x ) ,a ,tol ) * fx-7400G II : 3(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 Ax , 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 ).
AK4(CALC) * 2(
d / dx ) vMd+evx+v-g,
* fx-7400G
II : 3(CALC)
Input point
x = a for which you want to determine the derivative.
d,
Input the tolerance value.
bE-f)w
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 ,  ) 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.
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
'
