Find out the answer to "Find the derivative of ( 6 + 7..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Elle Weber

Answered question

2022-04-04

Find the derivative of

(6 + 7 x + 6 x^{2}) ﻿ x^{3}

Answer & Explanation

graffus1hb30

Beginner2022-04-05Added 15 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 $f (x) = 6 + 7 x + 6 x^{2}$ and $g (x) = x^{3}$ .

$(6 + 7 x + 6 x^{2}) \frac{d}{d x} [x^{3}] + x^{3} \frac{d}{d x} [6 + 7 x + 6 x^{2}]$

Differentiate.

$3 (6 + 7 x + 6 x^{2}) x^{2} + x^{3} (7 + 12 x)$

Simplify.

$30 x^{4} + 28 x^{3} + 18 x^{2}$

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