Ответ: f' ( π/2 ) = 13 .

Пошаговое объяснение:

f ( x ) = 7x - 6ctgx ; f' ( π/2 ) -?

f ' ( x ) = ( 7x - 6ctgx )' = (7x )' - ( 6ctgx )' = 7 + 6/sin²x ;

f ' ( x ) = 7 + 6/sin²x ; f' ( π/2 ) = 7 + 6/sin²( π/2) = 7 + 6 / 1² = 7 + 6 = 13 .