With f ( x ) = cos ⁡ ( π x 3 ) and g ( x ) = ln ⁡ ( x + 4 ), find the derivative of the quotient f ( x ) g ( x ) .

Set up the composite result function.g(f(x))Evaluate&nbsp;g(cos(πx3))&nbsp;by substituting in the value of&nbsp;f&nbsp;into&nbsp;g.g(cos(πx3))=ln((cos(πx3))+4)Remove parentheses.g(cos(πx3))=ln(cos(πx3)+4)

Key to "With f ( x ) = cos ⁡..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Waylon Mcbride

Answered question

2022-04-10

With

f (x) = \cos (\frac{π x}{3})

and

g (x) = \ln (x + 4)

, find the derivative of the quotient

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

Answer & Explanation

Allyson Gonzalez

Beginner2022-04-11Added 24 answers

Set up the composite result function.

$g (f (x))$

Evaluate $g (\cos (\frac{π x}{3}))$ by substituting in the value of $f$ into $g$ .

$g (\cos (\frac{π x}{3})) = \ln ((\cos (\frac{π x}{3})) + 4)$

Remove parentheses.

$g (\cos (\frac{π x}{3})) = \ln (\cos (\frac{π x}{3}) + 4)$

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