hi, we already know a function is

(A)differentiable at $\displaystyle a$ if

$\displaystyle \lim_{x \to a} \left[f(x) - f(a) / (x - a) \right]$ exists.

now consider f:R $\displaystyle \to $ R, f(x) = $\displaystyle x^n$, for some N E N. Using the definition of(A),how can we prove that f is differentiable and that f'(x) = $\displaystyle nx^{n-1}$?

help would be greatly appreciated here. thank you