University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 202: 58



Work Step by Step

Given $y=zcos^{-1}{z}-\sqrt{(1-z^2)}$ On differentiating both sides: $\frac{dy}{dz}=\frac{d(zcos^{-1}{z}-\sqrt{(1-z^2)})}{dz}$ $\frac{dy}{dz}=z{\frac{-1}{\sqrt{(1-z^2)}}}+cos^{-1}{z}-\frac{1}{2\sqrt{(1-z^2)}}\frac{d({(1-z^2)})}{dz}$ $\frac{dy}{dz}={\frac{-z}{\sqrt{(1-z^2)}}}+cos^{-1}{z}+\frac{z}{\sqrt{(1-z^2)}}$ $\frac{dy}{dz}=cos^{-1}{z}$
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