Prove that $d^n(x^n)/dx^n = n!$ by induction I need to prove that $d^n(x^n)/dx^n = n!$ by induction.
Any help?

If $f_{n} = x^{n}$, noting that $f_{0} = 1$. Taking an initial step to show that  $\dfrac{d^1}{dx^1}f_{n} = nf_{n-1}$ and continuing with a second: $\dfrac{d^2}{dx^2}f_{n} = n(n-1)f_{n-2}$. Now taking the nth step you can see that $\dfrac{d^n}{dx^n}f_{n} = n(n-1)(n-2)(n-3)...(n-(n-1))f_{0}$
Inductive step
if $k = n + 1$ then $\dfrac{d^{k}}{dx^{k}}f_{k} = (n+1)n\dfrac{d^{k-1}}{dx^{k-1}}f_{n} = k!$
