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based on an earlier version of the Wolfram Language.
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ND[expr, x, x0]
gives a numerical approximation to the derivative of expr with respect to x at the point x0.
ND[expr, {x, n}, x0]
gives a numerical approximation to the n^(th) derivative of expr.
  • The expression expr must be numeric when its argument x is numeric.
  • ND[expr, x, x0] is equivalent to ND[expr, {x, 1}, x0].
  • ND 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, ND needs to evaluate expr at x0.
  • If expr is not analytic in the neighborhood of x0, then the default method EulerSum 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 x0.