Evaluate f(x+h)-f(x)/h and simplify if f(x) = x^2-2x

f(x+h) = [(x + h)^2 - 2(x + h)] = [x^2 + 2xh + h^2 - 2x - 2h]

So we have

[f(x+h) - f(x)]/h =

[(x^2 + 2xh + h^2 - 2x - 2h) - x^2 + 2x]/ h =

(2xh + h^2 - 2h) / h  =

h (2x + h - 2) / h =

(2x + h - 2)

And if we let h → 0, then we have

2x - 2

And this is the "derivative" of f(x) = x^2 - 2x