Answer
$f'(x)=\dfrac{x+1}{2\sqrt{x^3}}.$
Work Step by Step
$\dfrac{d}{dx}(f(x))=\dfrac{d}{dx}(x^{\frac{1}{2}})-\dfrac{d}{dx}(x^{-\frac{1}{2}})\rightarrow$
$f'(x)=\frac{1}{2}(x^{-\frac{1}{2}})+\frac{1}{2}(x^{-\frac{3}{2}})=\dfrac{x+1}{2\sqrt{x^3}}.$
