Answer
$h^{\prime}(x)=-\displaystyle \frac{2}{x^{2}}+\frac{6}{x^{4}}-\frac{4}{x^{5}}$
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 $
--------------------------------
$h^{\prime}(x)=[2x^{-1}-2x^{-3}+x^{-4}]^{\prime}=... $Sum Rule,
$=[2x^{-1}]^{\prime}-[2x^{-3}]^{\prime}+[x^{-4}]^{\prime}=$... individually:
$[2x^{-1}]^{\prime}=...$Constant Multiple Rule
$=2[x^{-1}]^{\prime}$=...power rule...$=2(-1\displaystyle \cdot x^{-2})=-\frac{2}{x^{2}}$
$[2x^{-3}]^{\prime}=...$Constant Multiple Rule
$=2[x^{-3}]^{\prime}$=...power rule...$= 2(-3x^{-4})=-\displaystyle \frac{6}{x^{4}}$
$[x^{-4}]^{\prime}$=...power rule...$=-4x^{-5}=-\displaystyle \frac{4}{x^{5}}$
So
$h^{\prime}(x)=-\displaystyle \frac{2}{x^{2}}-(-\frac{6}{x^{4}})+(-\frac{4}{x^{5}})$
$h^{\prime}(x)=-\displaystyle \frac{2}{x^{2}}+\frac{6}{x^{4}}-\frac{4}{x^{5}}$
