Answered: "With f ( x ) = 6 x..."

Autumn Pham

Answered question

2022-05-13

With

f (x) = 6 x^{2} + x + 6

and

g (x) = 7 x^{3} + 5 x^{2} + 3 x + 7

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

glapaso7ng5

Beginner2022-05-14Added 13 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (7 x^{3} + 5 x^{2} + 3 x + 7)$ by substituting in the value of $g$ into $f$ .

$f (7 x^{3} + 5 x^{2} + 3 x + 7) = 6 {(7 x^{3} + 5 x^{2} + 3 x + 7)}^{2} + 7 x^{3} + 5 x^{2} + 3 x + 7 + 6$

Remove parentheses.

$f (7 x^{3} + 5 x^{2} + 3 x + 7) = 6 {(7 x^{3} + 5 x^{2} + 3 x + 7)}^{2} + 7 x^{3} + 5 x^{2} + 3 x + 7 + 6$

Simplify each term.

$f (7 x^{3} + 5 x^{2} + 3 x + 7) = 294 x^{6} + 420 x^{5} + 402 x^{4} + 768 x^{3} + 474 x^{2} + 252 x + 294 + 7 x^{3} + 5 x^{2} + 3 x + 7 + 6$

Simplify by adding terms.

$f (7 x^{3} + 5 x^{2} + 3 x + 7) = 294 x^{6} + 420 x^{5} + 402 x^{4} + 775 x^{3} + 479 x^{2} + 255 x + 307$

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