Find the derivative of f(g(x)), where f ( x ) = 5 x + 1 and g ( x ) = 2 x 4 + x 3 + 2 x 2 + 2 x.

Set up the composite result function.f(g(x))Evaluate&nbsp;f(2x4+x3+2x2+2x)&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(2x4+x3+2x2+2x)=5(2x4+x3+2x2+2x)+1Apply the distributive property.f(2x4+x3+2x2+2x)=5(2x4)+5x3+5(2x2)+5(2x)+1Simplify.f(2x4+x3+2x2+2x)=10x4+5x3+10x2+10x+1

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College
Calculus and Analysis
Differential Calculus
Derivatives

Carley Haley

Answered question

2022-04-10

Find the derivative of f(g(x)), where

f (x) = \sqrt{5 x + 1}

and

g (x) = 2 x^{4} + x^{3} + 2 x^{2} + 2 x

Answer & Explanation

Layne Bailey

Beginner2022-04-11Added 16 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (2 x^{4} + x^{3} + 2 x^{2} + 2 x)$ by substituting in the value of $g$ into $f$ .

$f (2 x^{4} + x^{3} + 2 x^{2} + 2 x) = \sqrt{5 (2 x^{4} + x^{3} + 2 x^{2} + 2 x) + 1}$

Apply the distributive property.

$f (2 x^{4} + x^{3} + 2 x^{2} + 2 x) = \sqrt{5 (2 x^{4}) + 5 x^{3} + 5 (2 x^{2}) + 5 (2 x) + 1}$

Simplify.

$f (2 x^{4} + x^{3} + 2 x^{2} + 2 x) = \sqrt{10 x^{4} + 5 x^{3} + 10 x^{2} + 10 x + 1}$

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