Task/25819886
-------------------
5. Найдите значение производной функции f (x) = 6sinx +tgx при x= -π/6
--------------------
f '(x) = (6sinx +tgx) ' =(6sinx) ' + (tgx) ' =6(sinx) ' +1/cos²x = 6cosx +1/cos²x .
---
f ' (π/6) =6cos(-π/6) +1/cos²(-π/6) =6cos(π/6)+1/cos²(π/6) =
6*(√3)/2 +1/ ( (√3) /2) )² =3√3 +1 / (3/4) =3√3 + 4/3.
ответ: 3√3 + 4/3 .