Question

Найдите f'(п/12), если f(x)=sin^2 x

Answer 1

$\mathrm{f}(x) = \sin^2(x)$

$\mathrm{f}'(x) = (\sin^2(x))' = 2\cdot\sin(x)\cdot\sin'(x) =$

$= 2\cdot\sin(x)\cdot\cos(x) = \sin(2x)$

$\mathrm{f}'(\frac{\pi}{12}) = \sin(2\cdot\frac{\pi}{12}) = \sin(\frac{\pi}{6}) =$

$= 0{,}5$