This involves a quick application of the power rule, which is [tex]f'(x)=nx^{n-1}[/tex].
First, it is helpful to rewrite [tex]f(x)=\sqrt{x}[/tex] as [tex]f(x)=x^{\frac{1}{2}}[/tex]. Remember that these are equivalent forms, but the latter is easier to use with the power rule.
We apply the power rule and simply:
[tex]\frac{1}{2}(x)^{(\frac{-1}{2})}=\dfrac{1}{2x^{1/2}} = \dfrac{1}{2 \sqrt{x} }[/tex]
