Найдите производную функции в точке X = 1 y = ∛ (x²) y = (x-12) ^15-7y=1 / (∛x²) y=3 / (x+10) ^10

Найдем производную функции и вычислим ее значение в точке x = 1:

1. y (x) = x^ (2/3);

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

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

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

y (1) = 2/3 / 1^ (1/3) = 2/3.

2. y (x) = (x - 12) ^15 - 7;

y' (x) = 15 * (x - 12) ^14;

y' (1) = 15 * (1 - 12) ^14;

y' (1) = 15 * ( - 11) ^14 = 15 * 11^14.

3. y (x) = 1 / x^ (2/3);

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

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

y' (x) = - 2/3 * x^ (-5/3);

y' (x) = - 2/3 / x^ (5/3);

y' (1) = - 2/3 / 1^ (5/3) = - 2/3.

4. y (x) = 3 / (x + 10) ^10;

y (x) = 3 * (x + 10) ^ (-10);

y' (x) = 3 * (-10) * (x + 10) ^ (-11);

y' (x) = - 30 / (x + 10) ^11;

y' (1) = - 30 / (1 + 10) ^11 = - 30 / 11^11.