Найдите производных следующих функций 1) 2) 3) 4) 5) 6)

Найдем производные следующих функций:

1) y = - 1/x ^ 2;

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

2) y = 3/x ^ (4/3);

y ' = (3/x ^ (4/3)) ' = 3 * (x ^ ( - 4/3)) ' = 3 * ( - 4/3) * x ^ ( - 4/3 - 1) = - 4 * x ^ ( - 7/3) = 4/x ^ (7/3);

3) y = 3/√x ^ 3;

y ' = 3 * (x ^ (3/2)) ' = 3 * 3/2 * x ^ (3/2 - 1) = 9/2 * x ^ (1/2);

4) y = 2 * x ^ 3 * 3√x;

y ' = 2 * (x ^ (3 + 1/3)) ' = 2 * (x ^ (10/3)) ' = 2 * 10/3 * x ^ (10/3 - 1) = - 20/3 * x ^ (7/3);

5) y = x ^ 4/√x;

y ' = (x ^ (4 - 1/2)) ' = (x ^ (7/2)) ' = 7/2 * x ^ (7/2 - 1) = 7/2 * x ^ (5/2);

6) y = 2 * x ^ 3/√x ^ 3;

y ' = 2 * (x ^ (3 - 3/2)) ' = (2 * x ^ (3/2)) ' = 2 * 3/2 * x ^ (3/2 - 1) = 3 * x ^ (1/2).