Question

Найти производную f(x) = =  (cos х + 1)/ (cos x - 1)

Answer 1

$\f(x)=frac{cos x+1}{cos x-1}\ f'(x)=frac{-sin x(cos x -1)-(cos x +1)(-sin x)}{(cos x-1)^2}\ f'(x)=frac{-sin x(cos x-1-cos x-1)}{(cos x-1)^2}\ f'(x)=frac{-sin x cdot(-2)}{(cos x-1)^2}\ f'(x)=frac{2sin x }{(cos x-1)^2}$

Answer 2

$(frac{cosx+1}{cosx-1})'=frac{(-sinx)(cosx-1)-(cosx+1)(-sinx)}{(cosx-1)^2}$=

=$frac{2sinx}{(cosx-1)^2}$