Решите производные) 1. y=2-3x^2-x^3 2. y = (x+1) ^2 (x-1) ^23. y=2x^3-3x^2-44. y=-x^3+3x^2-25. y = (x-1) ^2 (x-3) ^26. y=-2x+6+3^3 (x-3) ^27. y=0,25 (x^3 + 3x^2) - 58. y=6x-9x^3

Вычислим производные:

1. y = 2 - 3 * x^2 - x^3;

y ' = - 6 * x - 3 * x^2;

2. y = (x + 1) ^2 * (x - 1) ^2;

y ' = 2 * (x + 1) * (x - 1) ^2 + 2 * (x - 1) * (x + 1) ^2 = 2 * (x - 1) * (x + 1) * (x - 1 + x + 1) = 2 * (x - 1) * (x + 1) * 2 * x = 4 * x * (x - 1) * (x + 1);

3. y = 2 * x^3 - 3 * x^2 - 4;

y ' = 6 * x^2 - 6 * x;

4. y = - x^3 + 3 * x^2 - 25.

y ' = - 3 * x^2 + 6 * x;

5. y = (x - 1) ^2 * (x - 3) ^2;

y ' = 2 * (x - 1) * (x - 3) ^2 + 2 * (x - 3) * (x - 1) ^2 = 2 * (x - 1) * (x - 3) * (2 * x - 4);

6. y = - 2 * x + 6 + 3^3 * (x - 3) ^2;

y ' = - 2 + 27 * 2 * (x - 3) = - 2 + 54 * (x - 3) = 54 * x - 54 * 3 - 2 = 54 * x - 164;

7. y = 0,25 * (x^3 + 3 * x^2) - 5;

y ' = 0.25 * (3 * x^2 + 6 * x);

8. y = 6 * x - 9 * x^3;

y ' = 6 - 27 * x^2.