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

Set up the composite result function.g(f(x))Evaluate&nbsp;g(tan(πx3))&nbsp;by substituting in the value of&nbsp;f&nbsp;into&nbsp;g.g(tan(πx3))=6(tan(πx3))+7Multiply&nbsp;6&nbsp;by&nbsp;tan(πx3).g(tan(πx3))=6tan(πx3)+7

Explained: "With f ( x ) = tan ⁡..."

College
Calculus and Analysis
Differential Calculus
Derivatives

tiyakexdw4

Answered question

2022-05-11

With

f (x) = \tan (\frac{π x}{3})

and

g (x) = \sqrt{6 x + 7}

, find the derivative of the quotient

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

Answer & Explanation

Ayaan Gonzalez

Beginner2022-05-12Added 15 answers

Set up the composite result function.

$g (f (x))$

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

$g (\tan (\frac{π x}{3})) = \sqrt{6 (\tan (\frac{π x}{3})) + 7}$

Multiply $6$ by $\tan (\frac{π x}{3})$ .

$g (\tan (\frac{π x}{3})) = \sqrt{6 \tan (\frac{π x}{3}) + 7}$

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