mathematica exponential Nth derivative treated as an unknown function

问题

I'd like to create a list of Hankel functions, defined in terms of an Nth derivative, but the Nth order derivatives get treated in the way that is described in the docs under "Derivatives of unknown functions", and left unevaluated. Here's an example:

Clear[x, gaussianExponential]
gaussianExponential[x_] := Exp[- x^2]
FullSimplify[Derivative[2][gaussianExponential[x]]]

I get: (E^-x^2)^[Prime][Prime]

(instead of seeing the derivatives evaluated (and the final expressions are left unsimplified)).

Any idea what's going on here?

回答1:

The Derivative applies to the function symbol f, not to the function evaluated at a point f[x]. So what you want is

Clear[x, gaussianExponential]
gaussianExponential[x_] := Exp[-x^2]
Derivative[2][gaussianExponential][x]//FullSimplify

回答2:

The correct syntax is:

Clear[x, gaussianExponential]
gaussianExponential[x_] := Exp[-x^2]
FullSimplify[Derivative[2][gaussianExponential][x]]

来源：https://stackoverflow.com/questions/7669498/mathematica-exponential-nth-derivative-treated-as-an-unknown-function