Answer
$f^{\prime}(x)=8x^{3}+9x^{2}$
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:$\ \ \ [cf]^{\prime}(x)=cf^{\prime}(x)\\$
$\displaystyle \frac{d}{dx}(cx)=c,\ \ \ \ \ \frac{d}{dx}(c)=0\\$
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$f^{\prime}(x)=[2x^{4}+3x^{3}-1]^{\prime}$=... Sum Rule...
$=[2x^{4}]^{\prime}+[3x^{3}]^{\prime}-[1]^{\prime}$=...individually:
$[2x^{4}]^{\prime}$=... Constant Multiple Rule...
$=2[x^{4}]^{\prime}$=... Power Rule...
$=2(4x^{3})=8x^{3}$
$[3x^{3}]^{\prime}$=... Constant Multiple Rule...
$=3[x^{3}]^{\prime}$=... Power Rule...
$=3(3x^{2})=9x^{2}$
$[1]^{\prime}$=...(constant)'...=0
$f^{\prime}(x)=8x^{3}+9x^{2}$
