With f ( x ) = 2 x + 7 3 and g ( x ) = tan ⁡ ( π x 6 ), find the derivative of the compostion f(g(x)).

Set up the composite result function.f(g(x))Evaluate&nbsp;f(tan(πx6))&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(tan(πx6))=2(tan(πx6))+73Multiply&nbsp;2&nbsp;by&nbsp;tan(πx6).f(tan(πx6))=2tan(πx6)+73

Get the answer to "With f ( x ) = 2 x..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Jace Wright

Answered question

2022-05-13

With

f (x) = \sqrt[3]{2 x + 7}

and

g (x) = \tan (\frac{π x}{6})

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

Answer & Explanation

Arturo Wallace

Beginner2022-05-14Added 17 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (\tan (\frac{π x}{6}))$ by substituting in the value of $g$ into $f$ .

$f (\tan (\frac{π x}{6})) = \sqrt[3]{2 (\tan (\frac{π x}{6})) + 7}$

Multiply $2$ by $\tan (\frac{π x}{6})$ .

$f (\tan (\frac{π x}{6})) = \sqrt[3]{2 \tan (\frac{π x}{6}) + 7}$

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