Вариант 1. Задание 2. Вычислите производные при заданном значении аргумента: 1) $$f(x) = 4x^3 - 3x^2 - x - 1, f'(-1)$$. 2) $$f(x) = (2x^3 - 1)(x^2 + 1), f'(1)$$. 3) $$f(x) = \frac{x^3}{1 - x^2}, f'(2)$$.

1) $$f(x) = 4x^3 - 3x^2 - x - 1$$ $$f'(x) = 12x^2 - 6x - 1$$ $$f'(-1) = 12(-1)^2 - 6(-1) - 1 = 12 + 6 - 1 = 17$$ 2) $$f(x) = (2x^3 - 1)(x^2 + 1)$$ $$f'(x) = (6x^2)(x^2+1) + (2x^3-1)(2x) = 6x^4 + 6x^2 + 4x^4 - 2x = 10x^4 + 6x^2 - 2x$$ $$f'(1) = 10(1)^4 + 6(1)^2 - 2(1) = 10 + 6 - 2 = 14$$ 3) $$f(x) = \frac{x^3}{1 - x^2}$$ $$f'(x) = \frac{3x^2(1-x^2) - x^3(-2x)}{(1-x^2)^2} = \frac{3x^2 - 3x^4 + 2x^4}{(1-x^2)^2} = \frac{3x^2 - x^4}{(1-x^2)^2}$$ $$f'(2) = \frac{3(2)^2 - (2)^4}{(1 - (2)^2)^2} = \frac{12 - 16}{(1 - 4)^2} = \frac{-4}{(-3)^2} = -\frac{4}{9}$$