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NUMERICAL CALCULUS PACKAGE SYMBOL
ND
gives a numerical approximation to the derivative of expr with respect to x at the point 
.
gives a numerical approximation to the 
derivative of expr.
Details
- To use
, you first need to load the Numerical Calculus Package using Needs["NumericalCalculus`"]. - The expression expr must be numeric when its argument x is numeric.
is equivalent to 
.
is unable to recognize small numbers that should in fact be zero. Chop may be needed to eliminate these spurious residuals.- The following options can be given:
-
Method EulerSum method to use Scale 1 size at which variations are expected Terms 7 number of terms to be used WorkingPrecision MachinePrecision precision to use in internal computations - Possible settings for Method include:
-
EulerSum use Richardson's extrapolation to the limit NIntegrate use Cauchy's integral formula - With Method->EulerSum,
needs to evaluate expr at 
. - If expr is not analytic in the neighborhood of
, then the default method 
must be used. - The option Scale->s is used to capture the scale of variation when using Method->EulerSum.
- When the value of the derivative depends on the direction, the default is to the right. Other directions can be chosen with the option Scale->s, where the direction is s.
- The option Terms->n gives the number of terms to use for extrapolation when using Method->EulerSum.
- With Method->NIntegrate, the expression expr must be analytic in a neighborhood of the point
. - The option Scale->r specifies the radius of the contour of integration to use with Method->NIntegrate.
