Найдите производную функции y=1/x+3cosx

y = 1 / x + 3 * cos x = x ^ ( - 1 ) + 3 * cos x ; Производная y = ( x ^ ( - 1 ) + 3 * cos x ) \' = ( x ^ ( - 1 ) ) \' + ( 3 * cos x ) \' = ( x ^ ( - 1 ) ) \' + 3 * ( cos x ) \' = - 1 * x ^ ( - 1 - 1 ) + 3 * ( cos x ) \' = - 1 * x ^ ( - 2 ) + 3 * ( cos x ) \' = - x ^ ( - 2 ) + 3 * ( cos x ) \' = - x ^ ( - 2 ) + 3 * ( - sin x ) = - x ^ ( - 2 ) - 3 * sin x = - 1 / x ^ 2 - 3 * sin x ; Ответ: ( у ) \' = - 1 / x ^ 2 - 3 * sin x.