Find the derivative of f ( x ) g ( x ) , where f ( x ) = 2 x 2 + 3 and g ( x ) = e 4 x + 5 .

Set up the composite result function.f(g(x))Evaluate&nbsp;f(e4x+5)&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(e4x+5)=2(e4x+5)2+3Multiply the exponents in&nbsp;(e4x+5)2.f(e4x+5)=2e8x+10+3

Expert Answer to "Find the derivative of f ( x )..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Derick Richard

Answered question

2022-05-12

Find the derivative of

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

, where

f (x) = 2 x^{2} + 3

and

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

Answer & Explanation

Ariella Bruce

Beginner2022-05-13Added 19 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (e^{4 x + 5})$ by substituting in the value of $g$ into $f$ .

$f (e^{4 x + 5}) = 2 {(e^{4 x + 5})}^{2} + 3$

Multiply the exponents in ${(e^{4 x + 5})}^{2}$ .

$f (e^{4 x + 5}) = 2 e^{8 x + 10} + 3$

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