Answer
$h^{\prime}(x)=\displaystyle \frac{0.1}{x^{1.2}}$
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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$h^{\prime}(x)=[-\displaystyle \frac{1}{2x^{0.2}}]^{\prime}=[-\frac{1}{2}x^{-0.2}]^{\prime}=...$Constant Multiple Rule$...$
$= -\displaystyle \frac{1}{2}[ x^{-0.2}]^{\prime}$=...power rule...$=$
$= -\displaystyle \frac{1}{2}(-0.2\cdot x^{-1.2})$
$= 0.1x^{-1.2}$
$h^{\prime}(x)=\displaystyle \frac{0.1}{x^{1.2}}$
