Question

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

Answer 1

(cosx*(1-cosx)-sinx*(1+sinx))/(1-cosx)^2=(cosx-cos^2x-sinx-sin^2x)/(1-cosx)^2

Answer 2

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