With f ( x ) = ln ⁡ ( 3 x + 7 ) and g ( x ) = 3 x + 4 , find the derivative of the product (f*g)(x).

Set up the composite result function.f(g(x))Evaluate&nbsp;f(3x+4)&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(3x+4)=ln(3(3x+4)+7)Multiply&nbsp;3&nbsp;by&nbsp;3x+4.f(3x+4)=ln(33x+4+7)

Question: "With f ( x ) = ln ⁡..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Kevin Snyder

Answered question

2022-05-13

With

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

and

g (x) = \sqrt{3 x + 4}

, find the derivative of the product (f*g)(x).

Answer & Explanation

Adeline Shah

Beginner2022-05-14Added 18 answers

Set up the composite result function.

$f (g (x))$

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

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

Multiply $3$ by $\sqrt{3 x + 4}$ .

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

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