Question Detail

Use the quotient rule, d/dx(u/v) = (v u' - u v') / v².Let u = 1 - cos x, so u' = sin x.Let v = 1 + cos x, so v' = -sin x.dy/dx = [(1+cos x)(sin x) - (1-cos x)(-sin x)] / (1+cos x)²dy/dx = [sin x + sin x cos x + sin x - sin x cos x] / (1+cos x)²dy/dx = [2 sin x] / (1+cos x)². Now, evaluate at x = π/2: sin(π/2) = 1cos(π/2) = 0dy/dx |_(x=π/2) = [2 * 1] / (1+0)² = 2 / 1 = 2.