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45
Differential Calculations Chapter 3
This average, which is called the central difference, is expressed as:
u u
u u u
To perform a differential calculation
Example To determine the derivative at point
x
= 3 for the function
y
=
x
3
+ 4
x
2
+
x
– 6, when the increase/decrease of
x
is defined as
∆ x
= 1
E
– 5
Input the function
f ( x )
.
A K 2
(CALC)
[ 1
(
d/dx
)
T M d+e T x
+ T -g,
Input point
x
=
a
for which you want to determine the derivative.
d,
Input
∆ x
, which is the increase/decrease of
x
.
b E- f)
w
• In the function
f ( x )
, only X can be used as a variable in expressions. Other vari-
ables (A through Z) are treated as constants, and the value currently assigned to
that variable is applied during the calculation.
• Input of
∆
x
and the closing parenthesis can be omitted. If you omit
∆
x
, the calcu-
lator automatically uses a value for
∆ x
that is appropriate for the value of
x
=
a
,
which you specified as the point for which you wanted to determine the deriva-
tive.
• Discontinuous points or sections with drastic fluctuation can adversely affect pre-
cision or even cause an error.
• Note that you cannot use differential calculation inside of a differential calculation
term.
1 f ( a +
∆
x ) – f ( a ) f ( a ) – f ( a –
∆
x )
f '( a ) = –– ––––––––––––– + –––––––––––––
2 ∆
x
∆
x
f ( a +
∆
x ) – f ( a –
∆
x )
=
–––––––––––––––––
2 ∆
x