CODEWITHSUNDEEP
wolfram-mathematica
Peeter Joot
Peeter Joot

Reputation: 8260

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

Any idea what's going on here?

Upvotes: 0

Views: 1133

Answers (2)

Dr. belisarius
Dr. belisarius

Reputation: 61046

The correct syntax is: 

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

Upvotes: 5

Simon
Simon

Reputation: 14731

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

Upvotes: 4

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