Consider a discrete map
$x(t+1) = f(x(t)), \quad\forall t\in \mathbb{Z}$
For example, $f(x(t)) = (x(t))^3$.
From searching Wikipedia on forward difference, the discrete equilvalent of the derivative can be a (forward) difference $\Delta{f(x(t))} = f(x(t+1)) - f(x(t)) = (x(t+1))^3 - (x(t))^3$.
From some online sources (See section 4.1 just below equation (7) from: http://www.wisdom.weizmann.ac.il/~vered/CourseDS2019/Tutorial%203%20-%201d%20maps.pdf), I can infer that it would be just $3(x(t))^2$.
Which way is correct?