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llunallenaipg5r

Answered question

2022-04-10

Find the derivative of (f*g)(x), where

f (x) = 2 x^{2} + 3

and

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

stormiinazlhdd

Beginner2022-04-11Added 12 answers

Set up the composite result function.

$f (g (x))$

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

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

Simplify each term.

$f (7 x^{3} + 3 x + 5) = 98 x^{6} + 84 x^{4} + 140 x^{3} + 18 x^{2} + 60 x + 50 + 3$

Add $50$ and $3$ .

$f (7 x^{3} + 3 x + 5) = 98 x^{6} + 84 x^{4} + 140 x^{3} + 18 x^{2} + 60 x + 53$

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