Answered: "Find the derivative of (f*g)(x), where f (..."

Merati4tmjn

Answered question

2022-05-13

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

f (x) = \ln (7 x + 3)

and

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

Marco Meyer

Beginner2022-05-14Added 16 answers

Set up the composite result function.

$f (g (x))$

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

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

Simplify each term.

$f (x^{4} + x^{3} + x^{2} + 2 x + 6) = \ln (7 x^{4} + 7 x^{3} + 7 x^{2} + 14 x + 42 + 3)$

Add $42$ and $3$ .

$f (x^{4} + x^{3} + x^{2} + 2 x + 6) = \ln (7 x^{4} + 7 x^{3} + 7 x^{2} + 14 x + 45)$

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?