Is my derivative for the Wigner function of Fock States correct?

[Muthumanimaran]

Homework Statement

Currently I am doing a problem of finding Wigner function for Fock States, while I got this derivative, I found the derivative, but I am not sure my answer is correct. please verify whether my answer is correct or not.

$$ \frac{∂^2n}{∂β^n∂(β*)^n} exp(-|β|^2-4|α||β|) $$

β and α are complex.

Homework Equations

The Attempt at a Solution

My solution is (-2|β|-4|α|)^(2n) exp(-|β|^2-4|α||β|)

 

[Muthumanimaran]

Thank you, I found the Wigner function for Fock States in a different way. But still I don't know how to solve the differentiation I mentioned above.