Question

Найти производную данной функции
(1+x)^3 * (1-x/2)^2 = f(x)

Answer 1

f'(x)=((1+x)³ *(1-x/2)²)'=((1+x)³)' *(1-x/2)²+((1-x/2)²)' *(1+x)³=3*(1+x)² *(1+x)' *(1-x/2)²+2(1-x/2)*(1-x/2)' *(1+x)³=3*(1+x)² *1*(1-x/2)²+2*(1-x/2)*(-1/2)*(1+x)³=3(1+x)² *(1-x/2)²-(1-x/2)*(1+x)³=((1+x)² *(1-x/2))*(3*(1-x/2)-(1+x))=(1+x)² *(1-x/2)*(2-2,5x)