Taking the derivative of what they gave x^(1/n)-(x-1)^(1/n),

I got:

(1/n)[(x^((1-n)/n))-(x-1)^((1-n)/n)). How do I show that this is decreasing?

I'm assuming that then I can say that using this,

a=x

b=x-1 (since b is less than a)

and use the derivatives accordingly. Also how can I conclude that the right side is less than the left in the original equation I want to prove? Is it just because it's decreasing?