Answer to Question #8300 in Real Analysis for mike

Question

if f(x)=x, show that f'(a)=1 for all a.

Answer 1

Let's calculate this derivative directly:

f'(x) = lim [(f(x+Δx) - f(x)) / Δx] = lim [(x + Δx - x) / Δx] = lim [Δx / Δx] = 1.