Question

найти производную y=sin(x/2)+cos(x/2)

Answer 1

$y=Sin \frac{x}{2}+Cos \frac{x}{2}\\\\y'=(Sin \frac{x}{2})'+(Cos \frac{x}{2})'=Cos \frac{x}{2}*( \frac{x}{2})'-Sin \frac{x}{2}*( \frac{x}{2})'= \frac{1}{2}Cos \frac{x}{2} -$$\frac{1}{2}Sin \frac{x}{2}= \frac{1}{2}(Cos \frac{x}{2} -Sin \frac{x}{2})$