Найти первую производную от функций: 1) f (x) = корень из х + 1/х + 1 2) f (x) = х^ (3/2) - х^ (-3/2) 3) f (x) = (x-3) ^ (3) (x-1) 4) f (x) = (x^ (2) - 9) (x+1)

Найдем первую производную от функций:

1) f (x) = √ (х + 1/х + 1);

f ' (x) = (√ (х + 1/х + 1)) ' = 1 / (2 * √ (х + 1/х + 1)) * (х + 1/х + 1) ' = 1 / (2 * √ (х + 1/х + 1)) * (1 - 1/х ^ 2 + 0) = 1 / (2 * √ (х + 1/х + 1)) * (1 - 1/х ^ 2);

2) f (x) = х ^ (3/2) - х ^ (-3/2);

f (x) = (х ^ (3/2) - х ^ (-3/2)) ' = 3/2 * x ^ (3/2 - 1) + 3/2 * x ^ ( - 3/2 - 1) = 3/2 * x ^ (1/2) + 3/2 * x ^ ( - 5/2);

3) f (x) = (x - 3) ^ (3);

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

4) f (x) = (x - 1);

f ' (x) = (x - 1) ' = 1 - 0 = 1;

4) f (x) = (x ^ (2) - 9);

f ' (x) = 2 * x - 0 = 2 * x;

5) f (x) = (x + 1);

f ' (x) = 1 + 0 = 1.