Given the functions f ( x ) = 6 x + 2 3 and g ( x ) = e 5 x + 7 , compute f(g(x))'.

Set up the composite result function.f(g(x))Evaluate&nbsp;f(e5x+7)&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(e5x+7)=6(e5x+7)+23Factor&nbsp;2&nbsp;out of&nbsp;6e5x+7+2.f(e5x+7)=2(3e5x+7+1)3

Step by step solution to "Given the functions f ( x ) =..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Yaritza Oneill

Answered question

2022-05-12

Given the functions

f (x) = \sqrt[3]{6 x + 2}

and

g (x) = e^{5 x + 7}

, compute f(g(x))'.

Answer & Explanation

Kylan Simon

Beginner2022-05-13Added 17 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (e^{5 x + 7})$ by substituting in the value of $g$ into $f$ .

$f (e^{5 x + 7}) = \sqrt[3]{6 (e^{5 x + 7}) + 2}$

Factor $2$ out of $6 e^{5 x + 7} + 2$ .

$f (e^{5 x + 7}) = \sqrt[3]{2 (3 e^{5 x + 7} + 1)}$

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