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"Just like how taking the derivative of a function gives you the slope, a derivative in finance is a bet on the rate of change of the value of a stock, or a bond, or an index."

No. That is just completely wrong. A derivative is a financial instrument that derives value from other things.

As an aside, the derivatives market is far bigger than the stock market.

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Derivatives is a difficult to asses market, in terms of size. For example, the largest derivatives markets out there - interest rate swaps - trade contracts that usually have ~zero net value at the beginning of their lives, when the sides open the contract. Derivatives typically start small and sometimes end up huge.

The investable universe looks something like that:

https://imgur.com/a/68U3LsZ

I think the writer was trying to write something cute and smart there with that connection, if only it was actually correct.

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