mathematica exponential Nth derivative treated as an unknown function

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 deriv开发者_如何学Pythonatives evaluated (and the final expressions are left unsimplified)).

Any idea what's going on here?

The correct syntax is:

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

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