Найти производную функции f (x) = (x-4) ctgx

(u*v) ' = u'*v+u*v'

f ' (x) = ((x-4) * ctg (x)) ' = (x-4) '*ctg (x) + (x-4) * ctg' (x) = W

(u/v) ' = (u'*v - u*v') / (v^2)

ctg' (x) = (cos (x) / sin (x)) ' = ((cos (x)) '*sin (x) - cos (x) * (sin (x)) ') / (sin^2 (x) =

= (-sin^2 (x) - cos^2 (x)) / (sin^2 (x)) = - 1 / (sin^2 (x)).

W = ctg (x) + (x-4) * (-1/sin^2 (x)) = ctg (x) - ((x-4) / sin^2 (x)).