Answer
$g^{\prime}(x)=-\displaystyle \frac{1}{x^{2}}+\frac{2}{x^{3}}$
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 $
--------------------------------
$g^{\prime}(x)=[x^{-1}-x^{-2}]^{\prime}=... $Sum Rule,
$=[x^{-1}]^{\prime}-[x^{-2}]^{\prime}=$... individually:
$[x^{-1}]^{\prime}$=...power rule...$=-1\cdot x^{-2}=-x^{-2}$
$[x^{-2}]^{\prime}$=...power rule...$=-2x^{-3}$
So
$g^{\prime}(x)=-x^{-2}-(-2x^{-3})$
$g^{\prime}(x)=-x^{-2}+2x^{-3}$
