Вычислите производные функций y=f (x)

a) f (x) = - sin 2x - cos 2x

b) f (x) = x²+2cos x

c) f (x) = x³-tg 4x

d) f (x) = 2ctg 3x + 0.5x^4

ответы

a) 2 (sin2x-cos2x)

b) 2 (x-sinx)

а)

f' (x) = - cos2x * (2x) ' - (-sin2x) * (2x) '=-2cos2x+2sin2x

б)

f' (x) = 2x-2sin x

c)

f' (x) = 2x-1/cos^2 (4x) * (4x) '=2x-4/cos^2 (4x)

d)

f' (x) = 2 * (-1/sin^2 (3x) * (3x) '+0.5*4x^3=-6/sin^2 (3x) + 2x^3