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

I need help showing this is decreasing for $\displaystyle x$>$\displaystyle 1$

Any suggestions? trying to do this with the derivative.

I get

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

Can I assume $\displaystyle x^\frac{1-n}{n}<(x-1)^\frac{1-n}{n}$, If so why?

Any help would greatly be appreciated.