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I have two tables x and y with x={673,674,675,...} and y={0,1,2,...} and delta=dx/dy. I would like to know how delta can be calculated knowing that delta is the derivative of x divided by the derivative of y.

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Perhaps something like this will be useful:

x = Range[10];
y = x^2;

Differences[y]/Differences[x]

(*{3, 5, 7, 9, 11, 13, 15, 17, 19}*)

or alternatively:

Divide @@@ Differences[{y, x} // Transpose]

(*{3, 5, 7, 9, 11, 13, 15, 17, 19}*)
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