Question

найти производную функции y = 1-sinx/1+cosx

Answer 1

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