We have an answer to "With f ( x ) = 7 x..."

tuehanhyd8ml

Answered question

2022-05-12

With

f (x) = 7 x^{2} ﻿ + 7 x + 2

and

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

, find the derivative of the compostion f(g(x)).

Charlie Powers

Beginner2022-05-13Added 13 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (x^{3} + 6 x^{2} + 7 x + 4)$ by substituting in the value of $g$ into $f$ .

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

Simplify each term.

$f (x^{3} + 6 x^{2} + 7 x + 4) = 7 x^{6} + 84 x^{5} + 350 x^{4} + 644 x^{3} + 679 x^{2} + 392 x + 112 + 7 x^{3} + 42 x^{2} + 49 x + 28 + 2$

Simplify by adding terms.

$f (x^{3} + 6 x^{2} + 7 x + 4) = 7 x^{6} + 84 x^{5} + 350 x^{4} + 651 x^{3} + 721 x^{2} + 441 x + 142$

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