Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises: 21

Answer

$f’(x) = 1$

Work Step by Step

$f(x) = (x^{\frac{1}{2}}+1)(x^{\frac{1}{2}}-1); $ $ x\geq 0 $ Product and Power Rules: $f’(x) = \frac{1}{2}( x^{-\frac{1}{2}})(x^{\frac{1}{2}}-1) + \frac{1}{2}( x^{-\frac{1}{2}})(x^{\frac{1}{2}}+1) $ $f’(x) = \frac{1}{2} (1-x^{-\frac{1}{2}}) + \frac{1}{2}(1+ x^{-\frac{1}{2}}) $ $f’(x) = \frac{1}{2} (1-x^{-\frac{1}{2}} + 1+ x^{-\frac{1}{2}}) $ $f’(x) = \frac{1}{2} (2) $ $f’(x) = 1 $
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