Answer
$g^{\prime}(x)=-2x^{-3}+3x^{-2}$
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 $
--------------------------------
$g^{\prime}(x)=[x^{-2}-3x^{-1}-2]^{\prime}=... $Sum Rule,
$=[x^{-2}]^{\prime}-[3x^{-1}]^{\prime}-[2]^{\prime}=$... individually:
$[x^{-2}]^{\prime}$=...power rule...$=-2x^{-3}$
$[3x^{-1}]^{\prime}=$...Constant Multiple Rule...
$=3[x^{-1}]^{\prime}=$...power rule...$=3(-1\cdot x^{-2})=-3x^{-2}$
$[2]^{\prime}=...$Constant$...=0$
So
$g^{\prime}(x)=-2x^{-3}-(-3x^{-2})-0$
$g^{\prime}(x)=-2x^{-3}+3x^{-2}$
