Thank you very much for the interesting responses in my previous question The Quotient exponential operator.
I have another complicated formula related to the previous one in the following
$$
\exp\left[-x\bigg(\frac{d}{dx}\bigg)^{2}+\frac{d}{dx}\right]\big(f(x)\big).
$$

I would like to develop this equation and decompose it using a reference or a Book: I have found this kind of operators in G. Dattoli and A. Torre's works. I inform everyone that the two researchers produce many papers and Books in the fields of Physics and mathematics, so that is very difficult to search and find the required response within their large numbers of papers. If someone can help me I will be very grateful.
Respectful regards.

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