Answer
$\frac{dr}{ds}=\frac{1-2r-2s}{2s-1}$
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:
$2r\times1+2s\frac{dr}{ds}-\frac{dr}{ds}-1+2s=0$
$2r+2s\frac{dr}{ds}-\frac{dr}{ds}-1+2s=0$
Move all terms with dr/ds to one side of the equation, and isolate dr/ds:
$2s\frac{dr}{ds}-\frac{dr}{ds}=1-2r-2s$
$\frac{dr}{ds}(2s-1)=1-2r-2s$
$\frac{dr}{ds}=\frac{1-2r-2s}{2s-1}$
