Answered: "Find the derivative of ( 1 + 7..."

College
Calculus and Analysis
Differential Calculus
Derivatives

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Answered question

2022-04-10

Find the derivative of

(1 + 7 x + x^{2}) ﻿ (6 + x^{2})

Answer & Explanation

Bria Berg

Beginner2022-04-11Added 11 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 $f (x) = 1 + 7 x + x^{2}$ and $g (x) = 6 + x^{2}$ .

$(1 + 7 x + x^{2}) \frac{d}{d x} [6 + x^{2}] + (6 + x^{2}) \frac{d}{d x} [1 + 7 x + x^{2}]$

Differentiate.

$2 (1 + 7 x + x^{2}) x + (6 + x^{2}) (7 + 2 x)$

Simplify.

$4 x^{3} + 21 x^{2} + 14 x + 42$

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