Найти значение производной функции: f (t) = sint + ctgt в точке t0=0,5 П

F' (t) = (sin (t)) ' + (ctg (t)) ' = W

(sin (t)) ' = cos (t),

(ctg (t)) ' = (cos (t) / sin (t)) ' = (-sin (t) * sin (t) - cos (t) * cos (t)) / sin^2 (t) =

= - 1/sin^2 (t),

W = cos (t) - (1/sin^2 (t)),

f' (t0) = cos (п/2) - (1/sin^2 (п/2)) = 0 - (1/1) = - 1.