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In the question https://mathematica.stackexchange.com/search?q=non+newtonian, I use "dstar" as acronym to multiplicative derivative. But in the standard literature the symbol i $f^\star$. How can I, if it is possible define this type of symbol and use it --- or $D^\star$

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Use the Notation package. You first need to run

Needs["Notation`"]

which brings up a palette that you can use to enter notation. Since this is hard to write down, I am posting a gif showing how it is done. Use Esc+star+Esc to get the $\star$ symbol.

enter image description here

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