Find the nth derivative of $\displaystyle f(x) = x^n$ by calculating the first few derivatives and observing the pattern that occurs.

So, here's what I've done so far:

$\displaystyle f'(x) = nx^{x-1})$

$\displaystyle f''(x) = n(n-1)x^{n-2}$

$\displaystyle f''(x) = (n^2-n)x^{n-2}$

$\displaystyle f'''(x) = (n^3-2n^2+2n)x^{n-3}$

$\displaystyle f^{(4)}(x) = (n^4 - 5n^3 + 8n^2 - 6n)x^{n-4}$

The pattern of the exponents is clear to me, but the pattern of the coefficients is not. Can anybody help me? Thanks.