Uniswap math

The slope of the line segment connecting these points is the (negative) average price that the trade is executed at:

İfade 14: "y" equals negative "p" Subscript, "e" "x" "e" "c" "u" "t" "i" "o" "n" , Baseline "x" plus "y" Subscript, "s" "t" "a" "r" "t" , Baseline plus "y" Subscript, "e" "n" "d" , Baseline left brace, "x" Subscript, "l" "o" "w" , Baseline less than or equal to "x" less than or equal to "x" Subscript, "h" "i" "g" "h" , Baseline , right brace

For infinitesimally small trades, the price is the slope of the tangent line at that point.

İfade 16: "y" equals negative "p" Subscript, "s" "t" "a" "r" "t" , Baseline times "x" plus 2 "y" Subscript, "s" "t" "a" "r" "t" , Baseline

İfade 17: "y" equals negative "p" Subscript, "e" "n" "d" , Baseline "x" plus 2 "y" Subscript, "e" "n" "d" , Baseline

Calculations

Other labels

İfade 46: left parenthesis, StartFraction, "x" Subscript, "e" "n" "d" , Baseline minus "x" Subscript, "s" "t" "a" "r" "t" , Baseline Over 2 , EndFraction plus "x" Subscript, "s" "t" "a" "r" "t" , Baseline , StartFraction, "y" Subscript, "e" "n" "d" , Baseline minus "y" Subscript, "s" "t" "a" "r" "t" , Baseline Over 2 , EndFraction plus "y" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis

İfade 47: left parenthesis, "x" Subscript, "s" "t" "a" "r" "t" , Baseline plus StartFraction, "x" Subscript, "i" "n" , Baseline Over 2 , EndFraction , "y" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis

İfade 48: left parenthesis, "x" Subscript, "s" "t" "a" "r" "t" , Baseline minus StartFraction, "x" Subscript, "o" "u" "t" , Baseline Over 2 , EndFraction , "y" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis

İfade 49: left parenthesis, "x" Subscript, "e" "n" "d" , Baseline , "y" Subscript, "s" "t" "a" "r" "t" , Baseline plus StartFraction, "y" Subscript, "i" "n" , Baseline Over 2 , EndFraction , right parenthesis

İfade 50: left parenthesis, "x" Subscript, "e" "n" "d" , Baseline , "y" Subscript, "s" "t" "a" "r" "t" , Baseline minus StartFraction, "y" Subscript, "o" "u" "t" , Baseline Over 2 , EndFraction , right parenthesis

İfade 51:

İfade 52:

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