Answer
$g^{\prime}(x)=-\displaystyle \frac{2}{x^{3}}-\frac{3}{x^{4}}$
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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$g^{\prime}(x)=[x^{-2}+x^{-3}]^{\prime}=... $Sum Rule,
$=[x^{-2}]^{\prime}+[x^{-3}]^{\prime}=$... individually:
$[x^{-2}]^{\prime}$=...power rule...$=-2x^{-3}$
$[x^{-3}]^{\prime}$=...power rule...$=-3x^{-4}$
$g^{\prime}(x)=-2x^{-3}+(-3x^{-4})$
$g^{\prime}(x)=-\displaystyle \frac{2}{x^{3}}-\frac{3}{x^{4}}$
