Question

помогите, пожалуйста, найти производную (tg(x)*cos(x))

Answer 1

y ' = (tgx * cosx) ' = (tgx) ' cosx + (cosx)' tgx = 
= 1/cos^2x * cosx - sinx* sinx/cosx = 
= 1 /cos x - sin^2x/ cosx = 
= (1 - sin^2x) / cosx = 
= cos^2x / cosx = 
= cosx