Given the functions f ( x ) = sin ⁡ ( π x 7 ) and g ( x ) = 6 x + 7 3 , compute the derivative of (f*g)(x).

Set up the composite result function.f(g(x))Evaluate&nbsp;f(6x+73)&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(6x+73)=sin(π(6x+73)7)Multiply&nbsp;π&nbsp;by&nbsp;6x+73.f(6x+73)=sin(π6x+737)

Question: "Given the functions f ( x ) =..."

College
Calculus and Analysis
Differential Calculus
Derivatives

et1wdwk4o

Answered question

2022-04-10

Given the functions

f (x) = \sin (\frac{π x}{7})

and

g (x) = \sqrt[3]{6 x + 7}

, compute the derivative of (f*g)(x).

Answer & Explanation

Layne Bailey

Beginner2022-04-11Added 16 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (\sqrt[3]{6 x + 7})$ by substituting in the value of $g$ into $f$ .

$f (\sqrt[3]{6 x + 7}) = \sin (\frac{π (\sqrt[3]{6 x + 7})}{7})$

Multiply $π$ by $\sqrt[3]{6 x + 7}$ .

$f (\sqrt[3]{6 x + 7}) = \sin (\frac{π \sqrt[3]{6 x + 7}}{7})$

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