Answer
$g^{\prime}(x)=-2x^{-2}-8x^{-3}$
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)=[2x^{-1}+4x^{-2}]^{\prime}=... $Sum Rule,
$=[2x^{-1}]^{\prime}+[4x^{-2}]^{\prime}=$... individually:
$[2x^{-1}]^{\prime}=$...Constant Multiple Rule...
$=2[x^{-1}]^{\prime}$=...power rule...$=2(-1\cdot x^{-2})=-2x^{-2}$
$[4x^{-2}]^{\prime}=$...Constant Multiple Rule...
$=4[x^{-2}]^{\prime}$=...power rule...$=4(-2x^{-3})=-8x^{-3}$
So
$g^{\prime}(x)=-2x^{-2}-8x^{-3}$
