2-24

IDifferential 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-7400GII: (CALC)

(a: point for which you want to determine the derivative, tol: tolerance) d/dx ( f (x), a)  dxd f (a)

The differentiation for this type of calculation is defined as:

f'(a) = lim

f (a +

Ax) – f (a)

–––––––––––––



Ax0

Ax

In this definition, infinitesimal is replaced by a sufficiently small x, with the value in the neighborhood of f' (a) calculated as:

f (a + x) – f (a)

f' (a) –––––––––––––A

x

A

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 = x3 + 4x2 + x – 6, with a tolerance of “tol” = 1E – 5

Input the function f(x).

*(CALC)* (d/dx)T,BCTVT E

* fx-7400GII: (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 1E–10.

•Specify a tolerance (tol) value of 1E–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.