Найти производную y=(x*(cos*ln*x+sin*ln*x))/2

Найдем производную y = (x * (cos (ln x) + sin (ln x)))/2. 

y \' = ((x * (cos (ln x) + sin (ln x)))/2) \' = 1/2 * (x \' * (cos (ln x) + sin (ln x)) + (cos (ln x) + sin (ln x)) \' * x) = 1/2 * (1 * (cos (ln x) + sin (ln x)) + (- sin (ln x)  * (ln x) \' + cos (ln x) * (ln x) \') * x) = 1/2 * (cos (ln x) + sin (ln x) + (- sin (ln x) * 1/x + cos (ln x) * 1/x)  * x) =  1/2 * (cos (ln x) + sin (ln x) - sin (ln x) * 1/x * x  + cos (ln x) * 1/x * x) =  1/2 * (cos (ln x) + sin (ln x) - sin (ln x)   + cos (ln x)) =  1/2 * (cos (ln x) + cos (ln x)) =  1/2 * 2 * cos (ln x) = cos (ln x); 

Ответ: y \' = cos (ln x).