Reference Guide

3-64 Full Command and Function Reference
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Incremental power mode must be set (flag –114 set).
Example: Find the fourth degree Taylor polynomial for the following:
x
3
4x 12+ +
11x
11
1+
-----------------------------
Command: DIVPC(X^3+4*X+12,11*X^11+1,4)
Result: 12+4*X+X^3
See also: TAYLOR0, TAYLR, SERIES
dn
Type: Function
Description: Differential of a function with respect to its argument n. For example d1f(x,y) is the differential of
f(x,y) with respect to x and d3g(y,z,t) is the differential of g(y,z,t) with respect to t. The second-
order derivative of f(x,y) with respect to x is written d1d1f(x,y). The dn function is an alternative
to the ∂ function; d1f(x,y) is the same as ∂x(f(x,y)). dn does not require brackets after it, it must be
followed immediately by the function name, with no spaces. dn differentiates with respect to the
whole of argument n, see the example. dn is mainly used for formal arguments, see the example in
DESOLVE, but can be used to differentiate expressions, as in the example.
Access: Access is by typing the letter “d” from the alpha keyboard, followed by the number n, before the
function whose differential is required.
Output: dn does not change its argument, it works like the negative sign placed before a number or an
expression. If the argument can be differentiated, N will carry out the differentiation.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example: Differentiate the function sin(2x) with respect to its argument:
Command: EVAL(d1SIN(2*X))
Result: COS(2*X)
(Note that the function was differentiated with respect to its argument 2x, not with respect to the
variable x.)
See also: DERIV, DERVX, DESOLVE, ∂
DO
Type: Command
Description: DO Indefinite Loop Structure Command: Starts DO…UNTIL…END indefinite loop structure.
DO … UNTIL … END executes a loop repeatedly until a test returns a true (nonzero) result.
Since the test clause is executed after the loop clause, the loop is always executed at least once.
The syntax is: DO loop-clause UNTIL test-clause END
DO starts execution of the loop clause. UNTIL ends the loop clause and begins the test clause.
The test clause must return a test result to the stack. END removes the test result from the stack.
If its value is zero, the loop clause is executed again; otherwise execution resumes following
END.
Access: !° BRANCH DO ( °is the left-shift of the Nkey).