Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5 - Page 151: 20


$\frac{d^2y}{dx^2}=\csc^3x+\cot^2x\csc x$

Work Step by Step

$y=cscx$ $\frac{dy}{dx}=−cotxcscx$ $\frac{d^2y}{dx^2}=−(\frac{d}{dx}(cotx)\times{cscx}+cotx\times{\frac{d}{dx}(cscx)})$ $\frac{d^2y}{dx^2}=−(−csc^2x\times{cscx}+cotx\times{−cotxcscx)}$ $\frac{d^2y}{dx^2}=\csc^3x+\cot^2x\csc x$
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