Question

Найти производную y '= 1 - cosx / 1+cosх

Answer 1

y=(1-cosx)/(1+cosx)=2sin²(x/2)/2cos²(x/2)=sin²(x/2)/cos²(x/2)=tg²(x/2);

 

y'=(tg²(x/2))'=2*(1/2)*tg(x/2)/cos²(x/2)=tg(x/2)/cos²(x/2)=sin(x/2)/cos³(x/2).