We are given that:

$\displaystyle f(x)=\displaystyle{\frac{(x-4)^2}{2x^\frac{1}{2}}}$

Show that:

$\displaystyle f'(x)=\displaystyle{\frac{3x^2-8x-16}{4x^\frac{3}{2}}}$

I've tried to figure this out and it just won't work!

Can anybody help please?