Question

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

Answer 1

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

Answer 2

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

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