Найдите значение производной.

sin^2x x0=pi/12

-x cos2x x0=0

1/2sin2x x0=pi/8

Y = sin²x.

u = sinx, v = u²

y' = u'·v' = (sinx) '·2u = 2sinx·cosx = sin2x

y' (x₀) = sin (2·π/12) = sin (π/6) = 1/2

y = - x·cos2x

y' = - (x) 'cos2x + - x· (cos2x) ' = - cos2x + 2x·sin2x

y' (x₀) = - cos0 + 0 = - 1

y = 1/2·sin2x

y' = 1/2·2cos2x = cos2x

y' (x₀) = cos (2·π/8) = cos (π/4) = √2/2