With f ( x ) = e 4 x + 5 and g ( x ) = tan ⁡ ( π x 4 ), find the derivative of the product (f*g)(x).

Set up the composite result function.f(g(x))Evaluate&nbsp;f(tan(πx4))&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(tan(πx4))=e4(tan(πx4))+5Multiply&nbsp;4&nbsp;by&nbsp;tan(πx4).f(tan(πx4))=e4tan(πx4)+5

Check the solution to "With f ( x ) = e 4..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Leon Robinson

Answered question

2022-05-12

With

f (x) = e^{4 x + 5}

and

g (x) = \tan (\frac{π x}{4})

, find the derivative of the product (f*g)(x).

Answer & Explanation

radcas87gex5r

Beginner2022-05-13Added 13 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (\tan (\frac{π x}{4}))$ by substituting in the value of $g$ into $f$ .

$f (\tan (\frac{π x}{4})) = e^{4 (\tan (\frac{π x}{4})) + 5}$

Multiply $4$ by $\tan (\frac{π x}{4})$ .

$f (\tan (\frac{π x}{4})) = e^{4 \tan (\frac{π x}{4}) + 5}$

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