The mathematical exponent of the Nth derivative is considered as an unknown function

Question

I would like to create a list of Hankel functions defined in terms of the Nth derivative, but Nth order derivatives are processed as described in the documents in the section "Derivatives of unknown functions", and left invaluable. Here is 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 left without help)).

Any idea what is going on here?

Answer 1

Derivative is applied to the symbol of the function f , and not to the function evaluated at the point f[x] . So you want

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

Answer 2

The correct syntax is:

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