With f ( x ) = ln ⁡ ( 5 x + 7 ) and g ( x ) = cos ⁡ ( π x 5 ), find the derivative of the compostion f(g(x)).

Set up the composite result function.f(g(x))Evaluate&nbsp;f(cos(πx5))&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(cos(πx5))=ln(5(cos(πx5))+7)Multiply&nbsp;5&nbsp;by&nbsp;cos(πx5).f(cos(πx5))=ln(5cos(πx5)+7)

Expert answers to "With f ( x ) = ln ⁡..."

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Calculus and Analysis
Differential Calculus
Derivatives

mars6svhym

Answered question

2022-05-13

With

f (x) = \ln (5 x + 7)

and

g (x) = \cos (\frac{π x}{5})

, find the derivative of the compostion f(g(x)).

Answer & Explanation

Lucille Lucas

Beginner2022-05-14Added 16 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (\cos (\frac{π x}{5}))$ by substituting in the value of $g$ into $f$ .

$f (\cos (\frac{π x}{5})) = \ln (5 (\cos (\frac{π x}{5})) + 7)$

Multiply $5$ by $\cos (\frac{π x}{5})$ .

$f (\cos (\frac{π x}{5})) = \ln (5 \cos (\frac{π x}{5}) + 7)$

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