ND


gives a numerical approximation to the derivative of expr with respect to x at the point .


gives a numerical approximation to the ^(th) derivative of expr.

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  • 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:
  • MethodEulerSummethod to use
    Scale1size at which variations are expected
    Terms7number of terms to be used
    WorkingPrecisionMachinePrecisionprecision to use in internal computations
  • Possible settings for Method include:
  • EulerSumuse Richardson's extrapolation to the limit
    NIntegrateuse 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.
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