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in this video im going to show you two ways to derive the spot price of a constant product amm such as uni swap b2 and b3 lets say that there are x amount of a and y amount of b inside the amm well define p as the spot price of b in terms of a in other words the exchange rate from a to b if i have one a then how much is it worth in b this spot price p is given by y divided by x the amount of b divided by the amount of a lets see why p is equal to y divided by x ill show you why this is so in two ways from geometry perspective and from calculus lets see why p is equal to y divided by x from geometry lets say that were trading on this curve x times y equals k so imagine uni swap b2 or unit swap b3 at the moment there are x amount of a and y amount of b so the current price is over here if we were to do a trade from a to b then we would put in some x amount of s that you can see over here and in return we get this much amount of b the slope of this green line is d y
