Answer
$f^{\prime}(x)=9x^{2}-4x+1$
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)=[3x^{3}-2x^{2}+x]^{\prime}=... $Sum Rule,
$=[3x^{3}]^{\prime}-[2x^{2}]^{\prime}+[x]^{\prime}=$... individually:
$[3x^{3}]^{\prime}...$Constant Multiple Rule$...$
$=3[x^{3}]^{\prime}$=...power rule...$=3(3x^{2})=9x^{2}$
$[2x^{2}]^{\prime}=...$Constant Multiple Rule$....$
$=2[x^{2}]^{\prime}$=...power rule...$=2(2x)=4x$
$[x]^{\prime}=[1\cdot x]^{\prime} ...$Constant times x$...=1$
$f^{\prime}(x)=9x^{2}-4x+1$
