Answer
$f'(x)=\frac{2}{\sqrt{1-(x-1)^2}}$
Work Step by Step
$f(x)=2\arcsin(x-1)$
$let$
$u=(x-1)$
$u'=1$
$\frac{d}{dx}(\arcsin u)= \frac{u'}{\sqrt{1-u^2}}$
$f'(u)=2\frac{u'}{\sqrt{1-u^2}}$
$f'(x)=\frac{2}{\sqrt{1-(x-1)^2}}$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.6 Exercises - Page 372: 39
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