Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - Review Exercises: 16

Answer

$\dfrac {2\left( x^{2}-x+1\right) }{x^{2}-2x+2} $

Work Step by Step

$\dfrac {d}{dx}\left( 2x\sqrt {x^{2}-2x+2}\right) =\left( \dfrac {d}{dx}\left( 2x\right) \right) \times \sqrt {x^{2}-2x+2}+\left( \dfrac {d}{dx}\sqrt {x^{2}-2x+2}\right) \times 2x=2\sqrt {x^{2}-2x+2}+\dfrac {1}{2}\times \dfrac {\left( 2x-2\right) }{\sqrt {x^{2}-2x+2}}\times 2x=\dfrac {2\left( x^{2}-2x+2+x-1\right) }{x^{2}-2x+2}=\dfrac {2\left( x^{2}-x+1\right) }{x^{2}-2x+2} $
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