f (x) = √2 x^2 - (3x-2) (5x+1) Найдите производные функции

Найдем производную функции f (x) = √2 * x^2 - (3 * x - 2) * (5 * x + 1).

f ' (x) = (√2 * x^2 - (3 * x - 2) * (5 * x + 1)) ' = (√2 * x^2) ' - ((3 * x - 2) * (5 * x + 1)) ' = √2 * 2 * x^ (2 - 1) - ((3 * x - 2) ' * (5 * x + 1) + (5 * x + 1) ' * (3 * x - 2)) = 2 * √2 * x - ((3 * 1 + 0) * (5 * x + 1) + (5 * 1 + 0) * (3 * x - 2)) = 2 * √2 * x - (3 * (5 * x + 1) + 5 * (3 * x - 2)) = 2 * √2 * x - (3 * 5 * x + 3 * 1 + 5 * 3 * x - 5 * 2) = 2 * √2 * x - (15 * x + 3 + 15 * x - 10) = 2 * √2 * x - (30 * x - 7) = 2 * √2 * x - 30 * x + 7.