Expert Answer to "Find the derivative of ( 5 + 4..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Adelyn Rodriguez

Answered question

2022-04-10

Find the derivative of

(5 + 4 x + 5 x^{2}) (6 + 4 x^{2})

Answer & Explanation

hospitaliapbury

Beginner2022-04-11Added 25 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 $f (x) = 5 + 4 x + 5 x^{2}$ and $g (x) = 6 + 4 x^{2}$ .

$(5 + 4 x + 5 x^{2}) \frac{d}{d x} [6 + 4 x^{2}] + (6 + 4 x^{2}) \frac{d}{d x} [5 + 4 x + 5 x^{2}]$

Differentiate.

$8 (5 + 4 x + 5 x^{2}) x + (6 + 4 x^{2}) (4 + 10 x)$

Simplify.

$80 x^{3} + 48 x^{2} + 100 x + 24$

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