Calculus (3rd Edition)

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

Chapter 3 - Differentiation - Chapter Review Exercises - Page 163: 42


$$ h'(z)=-\frac{3}{2}(z+(z+1)^{1/2})^{-5/2}\left(1+\frac{1}{2}(z+1)^{-1/2}\right) .$$

Work Step by Step

Recall that $(x^n)'=nx^{n-1}$ Since $ h(z)=(z+(z+1)^{1/2})^{-3/2}$, the derivative $ h'(z)$, by using the chain rule, is given by $$ h'(z)=-\frac{3}{2}(z+(z+1)^{1/2})^{-5/2}\left(1+\frac{1}{2}(z+1)^{-1/2}\right) .$$
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