Laila Andrews

2022-04-04

What is the derivative of $(5+6x+6{x}^{2})\ufeff{x}^{3}$?

rynosluv101swv2s

Beginner2022-04-05Added 19 answers

Differentiate using the Product Rule which states that $\frac{d}{dx}\left[f\left(x\right)g\left(x\right)\right]$ is $f\left(x\right)\frac{d}{dx}\left[g\left(x\right)\right]+g\left(x\right)\frac{d}{dx}\left[f\left(x\right)\right]$ where $f\left(x\right)=5+6x+6{x}^{2}$ and $g\left(x\right)={x}^{3}$.

$(5+6x+6{x}^{2})\frac{d}{dx}\left[{x}^{3}\right]+{x}^{3}\frac{d}{dx}[5+6x+6{x}^{2}]$

Differentiate.

$3(5+6x+6{x}^{2}){x}^{2}+{x}^{3}(6+12x)$

Simplify.

$30{x}^{4}+24{x}^{3}+15{x}^{2}$

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