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College
Calculus and Analysis
Differential Calculus
Derivatives

Laila Andrews

Answered question

2022-04-04

What is the derivative of

(5 + 6 x + 6 x^{2}) ﻿ x^{3}

Answer & Explanation

rynosluv101swv2s

Beginner2022-04-05Added 19 answers

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

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

Differentiate.

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

Simplify.

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

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