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})$