University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 3 - Section 3.11 - Linearization and Differentials - Exercises - Page 199: 29



Work Step by Step

We evaluate the function: $y=3\csc({1-2\sqrt{x}})$ on differentiating the above: $\frac{dy}{dx}=\frac{d(3\csc({1-2\sqrt{x}}))}{dx}$ or $\frac{dy}{dx}=-3\csc({1-2\sqrt{x}})\cot({1-2\sqrt{x}})\frac{d(({{1-2\sqrt{x}}})}{dx}$ or $\frac{dy}{dx}=\frac{3}{\sqrt{x}}\csc({1-2\sqrt{x}})\cot({1-2\sqrt{x}}))$ or ${dy}=\frac{3}{\sqrt{x}}\csc({1-2\sqrt{x}})\cot({1-2\sqrt{x}})){dx}$ The final answer is: ${dy}=\frac{3}{\sqrt{x}}\csc({1-2\sqrt{x}})\cot({1-2\sqrt{x}})){dx}$
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