Answer
$\frac{dr}{ds}=\frac{2rsin(2s)-sin(2s)}{cos(2s)}$
Work Step by Step
Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "r" variables since we are differentiating with respect to s:
$r\times-sin(2s)\times2+\frac{dr}{ds}cos(2s)+2sin(s)\times cos(s)\times1=0$
$-2rsin(2s)+\frac{dr}{ds}cos(2s)+sin(2s)=0$
Move all terms with dr/ds to one side of the equation, and isolate dr/ds:
$\frac{dr}{ds}cos(2s)=2rsin(2s)-sin(2s)$
$\frac{dr}{ds}=\frac{2rsin(2s)-sin(2s)}{cos(2s)}$
