Answer
$f^{\prime}(x)=-3x^{2}-6x^{2}$
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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$f^{\prime}(x)=[-x^{3}-3x^{2}-1]^{\prime}$=... Sum Rule...
$=[-x^{3}]^{\prime}-[3x^{2}]^{\prime}-[1]^{\prime}$=...individually:
$[-x^{3}]^{\prime}=[(-1)x^{3}]^{\prime}$=... Constant Multiple Rule...
$=-[x^{3}]^{\prime}$=... Power Rule...
$=-(3x^{2})=-3x^{2}$
$[3x^{2}]^{\prime}$=... Constant Multiple Rule...
$=3[x^{2}]^{\prime}$=... Power Rule...
$=3(2x^{1})=6x^{2}$
$[1]^{\prime}$=...(constant)'...=0
$f^{\prime}(x)=-3x^{2}-6x^{2}$
