Question

найти значение производной функции
$y = \sin( \frac{x}{2} )$
в точке
$x0 = \frac{\pi}{3}$
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Answer 1

y(x)=sin(x/2)

y'(x)=(sin(x/2)'*(x/2)'

y'(x)=cos(x/2)*(1/2)=cos(x/2) / 2

y'(π/3)=cos(π/6) / 2=√3/2 : 2=√3 / 4.