а) f(x) = 3x²

f'(x) = 6x

f'(x0) = 6*1 = 6

б) f(x) = cosx

f'(x) = -sinx

f'(x0) = - sin π/6 = -√3/2

в) f(x) = 2 + √x = 2 + x½

f'(x) = 1/2 x ^-½

f'(x0) = 1/2√4 = ¼

г) f(x) = x^5

f'(x) = 5x⁴

f'(x0) = 5*0⁴ = 5

д) f(x) = 2/x²

f'(x) = (2' * x² - 2 * 2x)/x⁴ = -4x/x⁴

f'(x0) = -4*1/1⁴ = -4

е) f(x) = 1/3x^5

f'(x) = (1' * 3x^5 - 1*(3x^5)'/9x^10 = 15x⁴/9x^10 = 5/3x^6

f'(x0) = 5/3(-1)^6 = 5/3

ж) f(x) = x^5/175

f'(x) = (5x⁴ * 175)/175² = 5x⁴/175 = x⁴/35

f'(x0) = 0⁴/35 = 0