Nope, it is not a Greek letter, notably it is not a lowercase delta. It is just some random made up symbol that looks like a letter D. Which is of course derived from delta, which is why it is all so damn confusing.
This notation is not so common in basic mathematics, but it is so incredibly convenient, especially with Einstein notation as shown at Section "Einstein notation for partial derivatives":
This notation is similar to partial label partial derivative notation, but it uses indices instead of labels such as , , etc.
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