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

Set up the composite result function.g(f(x))Evaluate&nbsp;g(cos(πx7))&nbsp;by substituting in the value of&nbsp;f&nbsp;into&nbsp;g.g(cos(πx7))=ln(6(cos(πx7))+7)Multiply&nbsp;6&nbsp;by&nbsp;cos(πx7).g(cos(πx7))=ln(6cos(πx7)+7)

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

College
Calculus and Analysis
Differential Calculus
Derivatives

Berghofaei0e

Answered question

2022-05-11

Given the functions

f (x) = \cos (\frac{π x}{7})

and

g (x) = \ln (6 x + 7)

, compute the derivative of

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

Answer & Explanation

Agrebbef4l93

Beginner2022-05-12Added 6 answers

Set up the composite result function.

$g (f (x))$

Evaluate $g (\cos (\frac{π x}{7}))$ by substituting in the value of $f$ into $g$ .

$g (\cos (\frac{π x}{7})) = \ln (6 (\cos (\frac{π x}{7})) + 7)$

Multiply $6$ by $\cos (\frac{π x}{7})$ .

$g (\cos (\frac{π x}{7})) = \ln (6 \cos (\frac{π x}{7}) + 7)$

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