Find the derivative of f(g(x)), where f x <mo stretchy="false">) = <msqrt> 5 x

Carley Haley

Carley Haley

Answered question

2022-04-10

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.

Answer & Explanation

Layne Bailey

Layne Bailey

Beginner2022-04-11Added 16 answers

Set up the composite result function.

f(g(x))

Evaluate f(2x4+x3+2x2+2x) by substituting in the value of g into f.

f(2x4+x3+2x2+2x)=5(2x4+x3+2x2+2x)+1

Apply the distributive property.

f(2x4+x3+2x2+2x)=5(2x4)+5x3+5(2x2)+5(2x)+1

Simplify.

f(2x4+x3+2x2+2x)=10x4+5x3+10x2+10x+1

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