Question

Найдите производную функции ƒ(х) = (1/3*х3) - (1/2*х2)

Answer 1

$f'(x)=[\frac{1}{3}*x^3-\frac{1}{2}*x^2]'=[\frac{1}{3}*x^3]'-[\frac{1}{2}*x^2]'=\\\\ =\frac{1}{3}*[x^3]'-\frac{1}{2}*[x^2]'=\frac{1}{3}*[3*x^{3-1}]-\frac{1}{2}*[2*x^{2-1}]=\\\\ =\frac{1}{3}*3*x^{2}-\frac{1}{2}*2*x^{1} =x^2-x$