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