Let $\displaystyle \sqrt{n}(\frac{Z_n}{\sqrt{2}n} - \frac{1}{\sqrt{2}})->N(0,1)$

We are interested in the square root of Zn. Let $\displaystyle g(t) = \sqrt{t}$ and let $\displaystyle W_n = g(\frac{Z_n}{\sqrt{2}n}) = \sqrt{(\frac{Z_n}{\sqrt{2}n})}$. I'm fine until here.

Not sure how they got:$\displaystyle g(1/ \sqrt{2}) = (1/2)^{1/4} \ \ \ g'(1/ \sqrt{2}) = 2^{-3/4}$. Could someone please explain this to me?