Given the functions f ( x ) = cos ⁡ ( π x 4 ) and g ( x ) = 2 x 3 + 6 x + 6, compute the derivative of f ( x ) g ( x ) .

Set up the composite result function.g(f(x))Evaluate&nbsp;g(cos(πx4))&nbsp;by substituting in the value of&nbsp;f&nbsp;into&nbsp;g.g(cos(πx4))=2cos3(πx4)+6(cos(πx4))+6Multiply&nbsp;6&nbsp;by&nbsp;cos(πx4).g(cos(πx4))=2cos3(πx4)+6cos(πx4)+6

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

College
Calculus and Analysis
Differential Calculus
Derivatives

Annabel Sullivan

Answered question

2022-05-13

Given the functions

f (x) = \cos (\frac{π x}{4})

and

g (x) = 2 x^{3} + 6 x + 6

, compute the derivative of

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

Answer & Explanation

Allyson Gonzalez

Beginner2022-05-14Added 24 answers

Set up the composite result function.

$g (f (x))$

Evaluate $g (\cos (\frac{π x}{4}))$ by substituting in the value of $f$ into $g$ .

$g (\cos (\frac{π x}{4})) = 2 \cos^{3} (\frac{π x}{4}) + 6 (\cos (\frac{π x}{4})) + 6$

Multiply $6$ by $\cos (\frac{π x}{4})$ .

$g (\cos (\frac{π x}{4})) = 2 \cos^{3} (\frac{π x}{4}) + 6 \cos (\frac{π x}{4}) + 6$

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