Log3 1/27 - log4 32 = log3 (3^-3) - log2^2 (32^5) = -3*log3 (3) - 5/2*log2 (2) = -3 - (5/2) = -(11/2) = -5,5
(4/3*(1/2)^3)/(2/9)^2= (4/3*1/8)/(4/81)=(1/6)/(4/81)=(1/6)*(81/4)=27/8=3,375
Дифференцирование произведения: (uv)' = u' v + u v'. Тут u(x) = x, v(x) = sin x.
f'(x) = x' sin x + x (sin x)' = sin x + x cos x
f'(x0) = sin(pi / 2) + pi/2 * cos(pi/2) = 1 + 0 = 1