Get the answer to "Given the functions f ( x ) =..."

William Santiago

Answered question

2022-05-13

Given the functions

f (x) = 7 x^{3} ﻿ + 3 x^{2} + 2 x + 7

and

g (x) = 7 x^{2} + 4

, compute the derivative of

\frac{f (x)}{g (x)}

parentalite50bqd

Beginner2022-05-14Added 12 answers

Set up the composite result function.

$g (f (x))$

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

$g (7 x^{3} + 3 x^{2} + 2 x + 7) = 7 {(7 x^{3} + 3 x^{2} + 2 x + 7)}^{2} + 4$

Simplify each term.

$g (7 x^{3} + 3 x^{2} + 2 x + 7) = 343 x^{6} + 294 x^{5} + 259 x^{4} + 770 x^{3} + 322 x^{2} + 196 x + 343 + 4$

Add $343$ and $4$ .

$g (7 x^{3} + 3 x^{2} + 2 x + 7) = 343 x^{6} + 294 x^{5} + 259 x^{4} + 770 x^{3} + 322 x^{2} + 196 x + 347$

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