Get the answer to "With f ( x ) = 6 x..."

lnwlf1728112xo85f

Answered question

2022-04-10

With

f (x) = 6 x^{2} + 4

and

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

, find the derivative of the quotient

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

Jerry Kidd

Beginner2022-04-11Added 18 answers

Set up the composite result function.

$g (f (x))$

Evaluate $g (6 x^{2} + 4)$ by substituting in the value of $f$ into $g$ .

$g (6 x^{2} + 4) = 5 {(6 x^{2} + 4)}^{3} + 7 {(6 x^{2} + 4)}^{2} + 6$

Simplify each term.

$g (6 x^{2} + 4) = 1080 x^{6} + 2160 x^{4} + 1440 x^{2} + 320 + 252 x^{4} + 336 x^{2} + 112 + 6$

Simplify by adding terms.

$g (6 x^{2} + 4) = 1080 x^{6} + 2412 x^{4} + 1776 x^{2} + 438$

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