Answer
$s^{\prime}(x)=\displaystyle \frac{1}{2\sqrt{x}}-\frac{1}{2x\sqrt{x}}$
Work Step by Step
SUMMARY:
The Power Rule$:\ \ \ [x^{n}]^{\prime}=nx^{n-1 } $
Sum Rule: $\ \ \ \ \ \ [f\pm g]^{\prime}(x)=f^{\prime}(x)\pm g^{\prime}(x) $
Constant Multiple Rule:$\ \ \ [cf]^{\prime}(x)=cf^{\prime}(x) $
Constant times x:$\ \ \ \displaystyle \frac{d}{dx}(cx)=c $
Constant:$\displaystyle \ \ \ \ \ \frac{d}{dx}(c)=0 $
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$s^{\prime}(x)=[x^{1/2}+x^{-1/2}]^{\prime}=... $Sum Rule,
$=[x^{1/2}]^{\prime}+[x^{-1/2}]^{\prime}=... $Power Rule,
$=\displaystyle \frac{1}{2}x^{-1/2}-\frac{1}{2}x^{-3/2}$
$s^{\prime}(x)=\displaystyle \frac{1}{2\sqrt{x}}-\frac{1}{2x\sqrt{x}}$
