Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.6 - The Chain Rule - Exercises 3.6 - Page 148: 12

Answer

$y'=\frac{-5}{2\sqrt x\times(\sqrt x/2-1)^{11}}$

Work Step by Step

Find y and u: $y=u^{-10}$ $u=\sqrt x/2-1$ First, find the derivative of y and u. Don't forget to apply chain rule for y': $y'=-10u^{-11}\times u'$ $u'=\frac{1}{4\sqrt x}$ Then plug in u and u' into y': $y'=-10(\sqrt x/2-1)^{-11}\times\frac{1}{4\sqrt x}=\frac{-5}{2\sqrt x\times(\sqrt x/2-1)^{11}}$
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