Given the functions f ( x ) = 4 x + 4 3 and g ( x ) = ln ⁡ ( 3 x + 3 ), compute the derivative of f ( x ) g ( x ) .

Set up the composite result function.g(f(x))Evaluate&nbsp;g(4x+43)&nbsp;by substituting in the value of&nbsp;f&nbsp;into&nbsp;g.g(4x+43)=ln(3(4x+43)+3)Factor&nbsp;4&nbsp;out of&nbsp;4x+4.g(4x+43)=ln(34(x+1)3+3)

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College
Calculus and Analysis
Differential Calculus
Derivatives

Carina Valenzuela

Answered question

2022-04-10

Given the functions

f (x) = \sqrt[3]{4 x + 4}

and

g (x) = \ln (3 x + 3)

, compute the derivative of

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

Answer & Explanation

Cara Cannon

Beginner2022-04-11Added 14 answers

Set up the composite result function.

$g (f (x))$

Evaluate $g (\sqrt[3]{4 x + 4})$ by substituting in the value of $f$ into $g$ .

$g (\sqrt[3]{4 x + 4}) = \ln (3 (\sqrt[3]{4 x + 4}) + 3)$

Factor $4$ out of $4 x + 4$ .

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

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