turunan dari R (t) = sint -cos t / cost + sin t adalah

R(t) = u / v
R'(t) = (u'v - uv') / v²

R(t) = (sin t - cos t) / (cos t + sin t)

R'(t) = [(cos t + sin t)(cos t + sin t) - (sin t - cos t)(-sin t + cos t)] / (cos t + sin t)²
=  [(cos t + sin t)² - (cos t - sin t)(sin t - cos t)] / (cos t + sin t)²
= [(1 + sin 2t) - (cos t sin t - cos² t - sin² t + cos t sin t)] / (1 + sin 2t)
= (1 + sin 2t) - (2 sin t cos t - 1) / (1 + sin 2t)
= (1 + sin 2t) - (sin 2t - 1) / (1 + sin 2t)
= 2 / (1 + sin 2t)