Найдите производную. y=cosx/1 + 2sinx

y = cos (x) / (1 + 2sin (x));

Производная частного:

(u / v) ' = (u'v - uv') / v^2;

y' = - sin (x) (1 + 2sin (x)) - cos (x) · 2cos (x)) / (1 + 2sin (x)) ^2 =

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

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