Answer
$f^{\prime}(x)=-1-\displaystyle \frac{1}{x^{2}}$
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:$\displaystyle \ \ \ \ \ \frac{d}{dx}(c)=0\\$
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$f^{\prime}(x)=[-x+\displaystyle \frac{1}{x}+1]^{\prime}$=... Sum Rule...
$=[-x]^{\prime}+[\displaystyle \frac{1}{x}]^{\prime}-[1]^{\prime}$=...individually:
$[-x]^{\prime}$=$[(-1)x]^{\prime}$... Constant times x... $=-1$
$[\displaystyle \frac{1}{x}]^{\prime}=[x^{-1}]^{\prime}$=... Power Rule...
$=-1(x^{-2})=-\displaystyle \frac{1}{x^{2}}$
$[1]^{\prime}$=...(constant)'...=0
$f^{\prime}(x)=-1-\displaystyle \frac{1}{x^{2}}$
