Найти производную функции y=(1+sinx)/(1-cosx)

Решите задачу:

$y=\frac{1+sin x}{1-cos x};\\\\y'=(\frac{1+sin x}{1-cos x})'=\frac{(1+sin x)'*(1-cos x)-(1+sin x)*(1-cos x)'}{(1-cos x)^2}=\\\\\frac{(0+cos x)(1-cos x)-(1+sin x)(0-(-sin x))}{(1-cos x)^2}=\\\\\frac{cos x(1-cos x)-(1+sin x)sin x}{(1-cos x)^2}=\\\\\frac{cos x-cos^2 x-sin x-sin^2 x }{(1-cos x)^2}=\\\\\frac{cos x-sin x-1}{(1-cos x)^2}$