Z=x+y/x-y частные производные

Question

Ева Захарова

Математика

2 июня, 03:59

Z=x+y/x-y частные производные

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Савелий Королев · Answer 1

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

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

1) (3 (x - 1) ^2) ' = 3 * (x - 1) ' * ((x - 1) ^2) ' = 3 * ((x) ' - (1) ') * ((x - 1) ^2) ' = 3 * (1 * x^ (1 - 1) - 0) * (2 * (x - 1) ^ (2 - 1)) = 6 (x - 1);

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

3) ((x - 1) ^3) ' = ((x - 1) ^3) ' = (x - 1) ' * ((x - 1) ^3) ' = ((x) ' - (1) ') * ((x - 1) ^3) ' = (1 * x^ (1 - 1) - 0) * (3 * (x - 1) ^ (3 - 1)) = 3 (x - 1) ^2;

4) (-2x^ (-3)) ' = (-2) * (-3) * x^ (-3 - 1) = 6 * x^ (-4) = 6x^ (-4).

y'' = ((3 (x - 1) ^2) * x^ (-2)) ' + (((x - 1) ^3) * (-2x^ (-3))) ' = (((3 (x - 1) ^2) ' * x^ (-2) + ((3 (x - 1) ^2) * (x^ (-2)) ') + (((x - 1) ^3) ' * (-2x^ (-3)) + ((x - 1) ^3) * (-2x^ (-3)) ') = (6 (x - 1) * x^ (-2) + ((3 (x - 1) ^2) * (-2x^ (-3))) + (((3 (x - 1) ^2) * (-2x^ (-3)) + ((x - 1) ^3) * (6x^ (-4))) = 6 (x - 1) * x^ (-2) + ((3 (x - 1) ^2) * (-2x^ (-3)) + ((3 (x - 1) ^2) * (-2x^ (-3)) + ((x - 1) ^3) * (6x^ (-4)) = 6 (x - 1) * x^ (-2) + ((6 (x - 1) ^2) * (-2x^ (-3)) + ((x - 1) ^3) * (6x^ (-4)) = 6 (x - 1) / x^2 - 12 (x - 1) ^2) / x^3 + 6 (x - 1) ^3 / x^4.