KermMartian at 19:17, 24 February 2016

2016-02-24T19:17:40Z

← Older revision		Revision as of 19:17, 24 February 2016
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	The exact formula that the calculator uses to evaluate this function is:		The exact formula that the calculator uses to evaluate this function is:

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\operatorname{nDeriv}(f(t),t,x,h)=\frac{f(x+h)-f(x-h)}{2h}		\operatorname{nDeriv}(f(t),t,x,h)=\frac{f(x+h)-f(x-h)}{2h}
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	(.001 is substituted for h when the argument is omitted)		(.001 is substituted for h when the argument is omitted)
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	* [[TI-BASIC:Fmin\|FMin(]]		* [[TI-BASIC:Fmin\|FMin(]]
	* [[TI-BASIC:Fmax\|FMax(]]		* [[TI-BASIC:Fmax\|FMax(]]
	* [[TI-BASIC:Fnint\|FnInt(]][[Category:TI-BASIC]]		* [[TI-BASIC:Fnint\|FnInt(]]
			[[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:15:17Z

Initial automated import

New page

{{Template:TI-BASIC:Command
|picture=NDERIV.GIF
|summary=Calculates the approximate numerical derivative of a function, at a point.
|syntax=nDeriv(''f''(''variable''),''variable'',''value''[,''h''])
|location=Press:
# MATH to access the [[TI-BASIC:Math|Math]] menu.
# 8 to select nDeriv(, or use arrows.
|compatibility=TI-83/84/+/SE
|size=1 byte
}}

nDeriv(''f''(''var''),''var'',''value''[,''h'']) computes an approximation to the value of the derivative of ''f''(''var'') with respect to ''var'' at ''var''=''value''. ''h'' is the step size used in the approximation of the derivative. The default value of ''h'' is 0.001.

nDeriv( only works for real numbers and expressions. nDeriv( can be used only once inside another instance of nDeriv(.

π→X
3.141592654
nDeriv(sin(T),T,X)
-.9999998333
nDeriv(sin(T),T,X,(abs(X)+e-6)e-6)
-1.000000015
nDeriv(nDeriv(cos(U),U,T),T,X)
.999999665

= Advanced =

If the default setting for ''h'' doesn't produce a good enough result, it can be difficult to choose a correct substitute. Although larger values of ''h'' naturally produce a larger margin of error, it's not always helpful to make ''h'' very small. If the difference between f(x+h) and f(x-h) is much smaller than the actual values of f(x+h) or f(x-h), then it will only be recorded in the last few significant digits, and therefore be imprecise.

A suitable compromise is to choose a tolerance ''h'' that's based on X. As suggested [http://www.unitedti.org/index.php?act=ST&f=54&t=4367&hl=&view=findpost&p=68526 here], (abs(X)+<span style="font-size: 80%">E</span>-6)<span style="font-size: 80%">E</span>-6 is a reasonably good value that often gives better results than the default.

= Formulas =

The exact formula that the calculator uses to evaluate this function is:

[[TI-BASIC:Math|Math]]
\operatorname{nDeriv}(f(t),t,x,h)=\frac{f(x+h)-f(x-h)}{2h}
[[TI-BASIC:/math|/math]]

(.001 is substituted for h when the argument is omitted)

= Error Conditions =

* '''[[TI-BASIC:Errors#domain|ERR:DOMAIN]]''' is thrown if h is 0 (since this would yield division by 0 in the formula)
* '''[[TI-BASIC:Errors#illegalnest|ERR:ILLEGAL NEST]]''' is thrown if nDeriv( commands are nested more than one level deep. Just having one nDeriv( command inside another is okay, though.

= Related Commands =

* [[TI-BASIC:Fmin|FMin(]]
* [[TI-BASIC:Fmax|FMax(]]
* [[TI-BASIC:Fnint|FnInt(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Nderiv - Revision history

KermMartian at 19:17, 24 February 2016

Maintenance script: Initial automated import