Answer
$f^{\prime}(x)=2x-3$
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 $
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$f^{\prime}(x)=[x^{2}-3x+5]^{\prime}=... $Sum Rule,
$=[x^{2}]^{\prime}-[3x]^{\prime}+[5]^{\prime}=$... individually:
$[x^{2}]^{\prime}$=...power rule...$=2x$
$[3x]^{\prime}=...$Constant times x$...=3$
$[5]^{\prime}= ...$Constant$...=0$
$f^{\prime}(x)=2x-3$
