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Productive investments are good for the economy.

Are they? Or are you defining "productive" circularly here?

If I'm wealthy and I invest in derivatives or complicated tranches, is that "productive" because it's enabling further circulation of money, or is it "productive" because I can gain more capital on it?

Given that there's an infinite supply of ever more derived tranches, I suspect that my definition of "productive" different from yours here.

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Digging down into what investment is, your are providing money to a person with the expectation that he will give you more back. Somehow, that extra has to be produced.

Analogously to a flying airplane - it is producing more lift than its weight. This must be true even if you haven't the slightest idea how all the whorls of air and eddies around it are created or how they influence the airplane.

What derivatives do is they spread risk in exchange for a lower rate of return, as well as provide liquidity. This is a productive thing that financial markets provide.

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