Calculus: Early Transcendentals (2nd Edition)

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

Chapter 3 - Derivatives - 3.3 Rules of Differentiation - 3.3 Exercises: 28

Answer

$h'(x)=1-(\frac{1}{2})x^{\frac{1}{2}}$

Work Step by Step

$h(x)=\sqrt x(\sqrt x-1)$ $h(x)=x^{\frac{1}{2}}(x^{\frac{1}{2}}-1)$ $u=x^{\frac{1}{2}}$ $u'=\frac{1}{2}x^{\frac{1}{2}-1}$ $u'=\frac{1}{2}x^{-\frac{1}{2}}$ $v=x^{\frac{1}{2}}-1$ $v'=\frac{1}{2}x^{\frac{1}{2}-1}-0$ $v'=\frac{1}{2}x^{-\frac{1}{2}}$ $h'(x)=u'v+uv'$ $h'(x)=\frac{1}{2}x^{-\frac{1}{2}}(x^{\frac{1}{2}}-1)+x^{\frac{1}{2}}(\frac{1}{2}x^{-\frac{1}{2}})$ $h'(x)=\frac{1}{2}x^{\frac{1}{2}-\frac{1}{2}}-\frac{1}{2}x^{-\frac{1}{2}}+\frac{1}{2}x^{\frac{1}{2}-\frac{1}{2}}$ $h'(x)=\frac{1}{2}-(\frac{1}{2})x^{\frac{1}{2}+\frac{1}{2}}$ $h'(x)=1-(\frac{1}{2})x^{\frac{1}{2}}$
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