Производные y=1-sin(x)/1+cos(x)

[latex]y'= (\frac{1-sin(x)}{1+cos(x)} )'= \frac{(1-sin(x))'*(1+cos(x))-(1-sin(x))*(1+cos(x))'}{1+cos^2(x)}[/latex] [latex]= \frac{-cos(x)*(1+cos(x))+sin(x)*(1-sin(x))}{(1+cos(x))^2} = \frac{-cos(x)-cos^2(x)+sin(x)-sin^2(x)}{(1+cos(x))^2}[/latex] =[latex] \frac{-1-cos(x)+sin(x)}{1+2cos(x)+cos^2(x)}[/latex]