2.(14) let f(x) Let15ƒ(x) = (2x² + 3) ¹ (2x² + 7) ¹5Find the derivative and write the answer in factored form.f'(x) =

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Answered: Let 15 ƒ(x) = (2x² + 3)¹ (2x² + 7) ¹5…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

2.(14) let f(x)

Let
15
ƒ(x) = (2x² + 3) ¹ (2x² + 7) ¹5
Find the derivative and write the answer in factored form.
f'(x) =

Expert Solution

Step 1: Derivatives rule

$f left parenthesis x right parenthesis equals left parenthesis 2 x squared plus 3 right parenthesis to the power of 7 left parenthesis 2 x squared plus 7 right parenthesis to the power of 15$

$left parenthesis 1 right parenthesis space fraction numerator d space over denominator d x end fraction left parenthesis x to the power of n right parenthesis equals n x to the power of n minus 1 end exponent left parenthesis 2 right parenthesis space fraction numerator d space over denominator d x end fraction left parenthesis c o n s tan t right parenthesis equals 0 left parenthesis 3 right parenthesis space fraction numerator d space over denominator d x end fraction left parenthesis a. b right parenthesis equals a cross times fraction numerator d space over denominator d x end fraction left parenthesis b right parenthesis plus b cross times fraction numerator d space over denominator d x end fraction left parenthesis a right parenthesis$