Answer
$r'=2(\frac{-sinθ}{(cosθ-1)^2})$
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: $cos^2θ+sin^2θ=1$
$=2(\frac{sinθ}{cosθ-1})\times\frac{-(cosθ-1)}{(cosθ-1)^2}$
$=2(\frac{-sinθ}{(cosθ-1)^2})$
