Get the answer to "With f ( x ) = 4 x..."

generiranfi7qu

Answered question

2022-05-12

With

f (x) = 4 x^{2} ﻿ + 2 x + 1

and

g (x) = 2 x^{3} + 1

, find the derivative of the product (f*g)(x).

charringpq49u

Beginner2022-05-13Added 23 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (2 x^{3} + 1)$ by substituting in the value of $g$ into $f$ .

$f (2 x^{3} + 1) = 4 {(2 x^{3} + 1)}^{2} + 2 (2 x^{3} + 1) + 1$

Simplify each term.

$f (2 x^{3} + 1) = 16 x^{6} + 16 x^{3} + 4 + 4 x^{3} + 2 + 1$

Simplify by adding terms.

$f (2 x^{3} + 1) = 16 x^{6} 20 x^{3} + 7$

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