Answer
$\displaystyle \frac{dy}{dx}=\frac{10.3x^{9.3}}{2}-\frac{99}{x^{2}}$
Work Step by Step
SUMMARY (rules in differential notation):
1. The Power Rule$:\ \ \ \displaystyle \frac{d}{dx}[x^{n}]=n\cdot x^{n-1 } $
2. Sum Rule: $\displaystyle \ \ \ \frac{d}{dx}[f\pm g](x)=\frac{d}{dx}[f(x)]\pm\frac{d}{dx}[g(x)] $
3. Constant Multiple Rule:$\ \ \displaystyle \frac{d}{dx}[cf(x)]=c\cdot\frac{d}{dx}[f(x)] $
4. Constant times x:$\ \ \ \displaystyle \frac{d}{dx}(cx)=c $
5. Constant:$\displaystyle \ \ \ \ \ \frac{d}{dx}(c)=0 $
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$\displaystyle \frac{dy}{dx}= \frac{d}{dx}[\frac{1}{2}x^{10.3}+99x^{-1})$ = $\ \ \ $...(2)
$=\displaystyle \frac{d}{dx}(\frac{1}{2}x^{10.3})+\frac{d}{dx}(99x^{-1})$ = $\ \ \ $...($3$)
$=\displaystyle \frac{1}{2}\frac{d}{dx}( x^{10.3})+99\frac{d}{dx}(x^{-1})$ = $\ \ \ $...($1,\ \ 6 $)
$=\displaystyle \frac{1}{2}(10.3x^{9.3})+99(-1\cdot x^{-2})$
$\displaystyle \frac{dy}{dx}=\frac{10.3x^{9.3}}{2}-\frac{99}{x^{2}}$