Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Practice Exercises - Page 178: 35



Work Step by Step

Take the derivative of the equation using Power Rule, Chain Rule, and Quotient Rule: $r'=2(\frac{sinθ}{cosθ-1})\times\frac{(cosθ-1)(cosθ)-(sinθ)(-sinθ-0)}{(cosθ-1)^2}$ $=2(\frac{sinθ}{cosθ-1})\times\frac{cos^2θ-cosθ+sin^2θ}{(cosθ-1)^2}$ Simplify using the Trigonometric Identity: $cos^2θ+sin^2θ=1$ $=2(\frac{sinθ}{cosθ-1})\times\frac{-(cosθ-1)}{(cosθ-1)^2}$ $=2(\frac{-sinθ}{(cosθ-1)^2})$
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