A1 a) ((2 - 3x)⁴)' = 4(2 - 3x)³ *(2 - 3x)' = -12(2 - 3x)³
б) (2/x² - Sinx)' = -2/x³ - Cosx
в) (Sinx -3Cosx)' = Cosx +3Sinx
г) (Cos(4x - π/3))' = -Sin(4x - π/3) * (4x - π/3)' = -4Sin(4x - π/3)
A2 f(x) = 0,5Sin(2x +π/6), f'(π/12) = ?
f'(x) = Cos(2x +π/6
f'(π/12) = Cos(2*π/12 + π/6) = Cosπ/3 = 1/2
B1 a) (x⁴Sinx)' = 4x³Sinx + x⁴Cosx
б) (2Sin²x + tgx)' = 4Sinx*Cosx + 1/Cos²x = 2Sin2x + 1/Cos²x
в) (√Cosx)' = 1/(2√Cosx) * (Cosx)' = -Sinx/(2√Cosx)
C1 f(x) = √(-x² +5x -4)
f'(x) = 1/(2√(-x² +5x -4) ) * (-x² +5x -4) ' = (-2x +5)/ (2√(-x² +5x -4) )