Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises - Page 127: 95



Work Step by Step

First Derivative: Using the quotient rule: $f’(x)=(\frac{u(x)}{v(x)})'=\frac{u'(x)v(x)-v'(x)u(x)}{(v(x))^2}$ $u(x)=x; u'(x)=1$ $v(x)=x-1; v'(x)=1$ $f'(x)=\frac{(1)(x-1)-(1)(x)}{(x-1)^2}=-\frac{1}{(x-1)^2}.$ Second Derivative: Using the quotient rule: $f’'(x)=\frac{d}{dx}f'(x)=(\frac{u(x)}{v(x)})'=\frac{u'(x)v(x)-v'(x)u(x)}{(v(x))^2}$ $u(x)=-1; u'(x)=0$ $v(x)=(x-1)^2; v'(x)=2(x-1)$ $f''(x)=\frac{(0)(x-1)^2-(-1)(2x-2)}{((x-2)^2)^2}=\dfrac{2}{(x-1)^3}.$
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