Find the derivative of (f*g)(x), where f ( x ) = ln ⁡ ( 5 x + 4 ) and g ( x ) = 7 x + 7 3 .

Set up the composite result function.f(g(x))Evaluate&nbsp;f(7x+73)&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(7x+73)=ln(5(7x+73)+4)Factor&nbsp;7&nbsp;out of&nbsp;7x+7.f(7x+73)=ln(57(x+1)3+4)

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Calculus and Analysis
Differential Calculus
Derivatives

rockandriot0odjn

Answered question

2022-05-11

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

f (x) = \ln (5 x + 4)

and

g (x) = \sqrt[3]{7 x + 7}

Answer & Explanation

Eliezer Olson

Beginner2022-05-12Added 16 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (\sqrt[3]{7 x + 7})$ by substituting in the value of $g$ into $f$ .

$f (\sqrt[3]{7 x + 7}) = \ln (5 (\sqrt[3]{7 x + 7}) + 4)$

Factor $7$ out of $7 x + 7$ .

$f (\sqrt[3]{7 x + 7}) = \ln (5 \sqrt[3]{7 (x + 1)} + 4)$

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